nLab Center for Quantum and Topological Systems

Contents
animated logo of CQTS

The Center for Quantum and Topological Systems (nyuad.nyu.edu/L.cqts) is a Research Center, launched in 2022, within the Research Institute of New York University in Abu Dhabi.

CQTS hosts cross-disciplinary research on topological quantum systems, such as topological phases of matter understood via holography and using tools from algebraic topology, ultimately aimed at addressing open questions in topological quantum computation. A unifying theme is the use of new methods from (persistent) Cohomotopy (aka framed Cobordism, aka absolute 𝔽 1 \mathbb{F}_1 -algebraic K-theory) and generalized Twisted Equivariant Differential (TED) cohomology, developed in string theory.


Contents


Conferences & Workshops




Jun 2022

Homotopical perspectives on Topological data analysis

Organizers: Sadok Kallel and Hisham Sati



Schedule for 02 June 2022:


  • 15:00 - 16:00 GST/UTC+4

    Ling Zhou (The Ohio State University, USA)

    Persistent homotopy groups of metric spaces

    By capturing both geometric and topological features of datasets, persistent homology has shown its promise in applications. Motivated by the fact that homotopy in general contains more information than homology, we study notions of persistent homotopy groups of compact metric spaces, together with their stability properties in the Gromov-Hausdorff sense. Under fairly mild assumptions on the spaces, we proved that the classical fundamental group has an underlying tree-like structure (i.e. a dendrogram) and an associated ultrametric. We then exhibit pairs of filtrations that are confounded by persistent homology but are distinguished by their persistent homotopy groups. We finally describe the notion of persistent rational homotopy groups, which is easier to handle but still contains extra information compared to persistent homology.


  • 16:00 - 17:00 GST/UTC+4

    Wojciech Chacholski (KTH, Sweden)

    Realisations of Posets

    My presentation is based on an article with the same title coauthored with A. Jin and F. Tombari (arXiv:2112.12209).

    Encoding information in form of functors indexed by the poset of rr-tuples of real numbers (persistence modules) is attractive for three reasons:

    a) metric properties of the poset are essential to study distances on persistence modules

    b) the poset of rr-tuples of real numbers has well behaved discrete approximations which are used to provide finite approximations of persistence modules

    c) the mentioned discretizations and approximations have well studied algebraic and homological properties as they can be identified with multi graded modules over polynomial rings.

    In my talk I will describe a construction called realisation, that transforms arbitrary posets into posets which satisfy all three requirements above and hence are particularly suitable for persistence methods.Intuitively the realisation associates a continuous structure to a locally discrete poset by filling in empty spaces. For example the realisation of the poset of natural numbers is the poset of non-negative reals. I will focus on illustrating how homological techniques, such as Koszul complexes, can be used to study persistence modules indexed by realisations.


  • 17:30 - 18:30 GST/UTC+4

    Grégory Ginot (Université Paris 13, France)

    Homotopical and sheaf theoretic point of view on multi-parameter persistence.

    In this talk we will highlight the study of level set persistence through the prism of sheaf theory and a special type of 2-parameter persistence: Mayer-Vietoris systems and a pseudo-symetry between those. This is based on joint work with Berkouk and Oudot.


  • 18:30 - 19:30 GST/UTC+4

    Rick Jardine (University of Western Ontario, Canada)

    Thoughts on big data sets

    This talk describes work in progress. The idea is to develop methods for analyzing a very large data sets X NX \subset \mathbb{R}^{N} in high dimensional spaces. There are well-known pitfalls to avoid, including the inability to computationally analyze TDA constructions for XX on account of its size, the “curse of high dimensionality”, and the failure of excision for standard TDA constructions. We discuss the curse of high dimensionality and define a hypercube metric on N\mathbb{R}^{N} that may lessen its effects. The excision problem for the Vietoris-Rips construction can be addressed by expanding the TDA discussion to filtered subobjects KK of Vietoris-Rips constructions. Unions of such subobjects satisfy excision in path components (clusters) and homology groups, by classical results. The near-term goal is to construct, for each data point xx, a “computable” filtered subcomplex K xV(X)K_{x} \subset V(X) with xK xx \in K_{x}, which would capture spatial local behaviour of the data set XX near xx. A large (but highly parallelizable) algorithm finds a nearest neighbour, or a set of kk-nearest neighbours for a fixed data point xXx \in X. Some variant of this algorithm may lead to a good construction of the local subcomplex K xK_{x}.


Jan 2023


\phantom{-----} [logo adapted from JMP 62 (2021) 042301]


Feb 2023

24 Feb 2023

CQTS and TII Workshop 2023

joint workshop with the Quantum Research Center (QRC) at the Technology Innovation Institute (TII) in Abu Dhabi

on quantum materials, quantum computation and quantum programming

Break: 10:40 - 11:10

Lunch: 13:00 – 2:15

  • 14:15 - 14:25

    Hisham Sati:

    Introducing research and researchers @CQTS

  • 14:30 - 14:50

    Amaria Javed:

    Quantum information processing via NLS

  • 15:00 - 15:20

    Marwa Mannaï:

    Tuning topological quantum materials

  • 15:30 - 15:50

    Mitchell Riley:

    Verified quantum programming with linear HoTT

Break: 3:50-4:20 pm


Mar 2023

15-18 Mar 2023

Geometric/Topological Quantum Field Theories and Cobordisms (webpage)

on functorial quantum field theory, knot homology and cobordism theory/cobordism categories/cobordism hypothesis

\phantom{-----} [logo adapted from arXiv:2103.01877]

\;\;

Mee Seong Im, Mikhail Khovanov, Vivek Singh, Sergei Gukov, Anna Beliakova, Khaled Qazaqzeh

Domenico Fiorenza, Carlo Collari, Sadok Kallel, Nafaa Chbili, Christian Blanchet, David Jaz Myers

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; Nitu Kitchloo, Daniel Berwick-Evans, Adrian Clough

Sachin Valera, Alonso Perez-Lona, Urs Schreiber \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; Daniel Grady, Christoph Schweigert

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; Hisham Sati, Konrad Waldorf, Dmitri Pavlov


  • Mikhail Khovanov (Columbia University):

    Universal construction, foams and link homology

    cf.: arXiv:1808.09662, arXiv:2011.11077

    video 1:YT, 2:YT

    In this series of three talks we will explain the foam approach to link homology. Bigraded link homology theories categorify the Jones polynomial and other Reshetikhin-Turaev link invariants, such as the HOMFLY-PT polynomial. Foams, which are polyhedral 2D complexes embedded in 3-space allow to construct state spaces for planar graphs which are then used to define link homology groups. The most explicit and efficient way to define graph state spaces is via evaluation of the closed foams (Robert-Wagner formula).

    A) This formula will be first explained in the less technical unoriented SL(3)SL(3) case. Resulting graph state spaces are then related to the Four-Color Theorem and Kronheimer-Mrowka homology for 3-orbifolds.

    B) A step in that construction requires building a topological theory (a lax TQFT) from an evaluation of closed objects, such as closed nn-manifolds. We will explain the setup for topological theories, including in two dimensions, recovering the Deligne categories and their generalizations. In one dimension and adding defects, these topological theories are related to noncommutative power series, pseudocharacters, and, over the Boolean semiring, to regular languages and automata.

    C) Robert-Wagner GL(N)GL(N) foam evaluation and its application to constructing link homology theories will be explained as well.





  • Arun Debray (Purdue University):

    Twisted string bordism and a potential anomaly in E 8×E 8E_8 \times E_8 heterotic string theory

    cf.: arXiv:2210.04911

    video: YT

    Quantum field theories can have an inconsistency called an anomaly, formulated as an invertible field theory in one dimension higher. Theorems of Freed-Hopkins-Teleman and Freed-Hopkins classify invertible field theories in terms of bordism groups. In this talk, I’ll apply this to the low-energy approximation of E 8×E 8E_8 \times E_8 heterotic string theory; Witten proved anomaly cancellation in a restricted setting, but we perform a twisted string bordism computation to show that the relevant group of 11-dimensional invertible field theories does not vanish, and therefore there could be an anomaly in E 8×E 8E_8 \times E_8 heterotic string theory. Standard computational techniques for twisted string bordism do not work for this problem; I will also discuss work joint with Matthew Yu using Baker-Lazarev’s R-module Adams spectral sequence to simplify a large class of twisted spin and string bordism computations.



  • Mee Seong Im (United States Naval Academy):

    Correspondence between automata and one-dimensional Boolean topological theories and TQFTs

    cf.: arXiv:2301.00700

    video: YT

    Automata are important objects in theoretical computer science. I will describe how automata emerge from topological theories and TQFTs in dimension one and carrying defects. Conversely, given an automaton, there’s a canonical Boolean TQFT associated with it. In those topological theories, one encounters pairs of a regular language and a circular regular language that describe the theory.






  • Nafaa Chbili (United Arab Emirates University):

    Quasi-alternating links, Examples and obstructions

    cf.: arXiv:2009.08624

    video: YT

    Quasi-alternating links represent an important class of links that has been introduced by Ozsváth and Szabó while studying the Heegaard Floer homology of the branched double-covers of alternating links. This new class of links, which share many homological properties with alternating links, is defined in a recursive way which is not easy to use in order to determine whether a given link is quasi-alternating. In this talk, we shall review the main obstruction criteria for quasi-alternating links. We also discuss how new examples of quasi-alternating links can constructed.


  • Khaled Qazaqzeh (Kuwait University):

    On the Finiteness of Quasi-alternating Links

    cf.: arXiv:2208.02984

    slides: pdf

    video: YT

    The generalization of alternating links to quasi-alternating links raises some natural questions that have affirmative answer in the class of alternating links.

    In this talk, we discuss these questions and then we give an affirmative answer to one question without any assumption. As a consequence, we prove that one of these questions is solved in the affirmative iff Green’s conjecture on the finiteness of quasi-alternating links of a given determinant holds. Also, we prove that another question is solved in the affirmative implies Green’s conjecture on the finiteness of quasi-alternating links of a given determinant holds.











Apr 2023


May 2023

22 - 26 May 2023

Quantum Information and Quantum Matter

> on quantum information, quantum matter

webpage


  • Luigi Amico, (Technology Innovation Institute, Abu Dhabi):

    Coherence of confined matter in lattice gauge theories at the mesoscopic scales

    Atomtronics is the emerging quantum technology of matter-wave circuits which coherently guide propagating ultra-cold atoms. The field benefits from the remarkable progress in micro optics, allowing to control the coherent matter with enhanced flexibility on the micron spatial scale. This way, both fundamental studies in quantum science and technological applications can be carried out. I will sketch recent progress in matter-wave circuitry and atomtronics-based quantum technology. In particular, I will focus on a specific scheme simulating lattice gauge theories and analyze confined matter at the mesoscopic spatial scale.



  • Herbert Schoeller (RWTH Aachen):

    Supersymmetry protected topological states and realization of periodic Witten models in two dimensional second-order topological insulators

    cf.: arXiv:2212.01307

    For a generic two-dimensional topological insulator with band inversion and spin-orbit coupling, we propose the generation of topological zero-energy bound states via the application of an in-plane Zeeman field breaking rotational invariance. The Zeeman field induces a surface gap and generates the topological states via a second-order mechanism generically at the surface positions where the normal component of the Zeeman field vanishes. Via the application of an additional half-integer Aharonov-Bohm flux through a hole of the system, we show that the topological states are protected by supersymmetry. For smooth surfaces, we derive an effective surface Hamiltonian in the form of a periodic Witten model and propose how the surface bound states of the supersymmetric spectrum can be calculated via a trapping mechanism in effective surface potentials. We study the whole phase diagram of the model together with its stability and discuss the high tunability of the topological states.



  • Markus Müller (RWTH Aachen University and Forschungszentrum Jülich, Germany):

    Fault-Tolerant Topological Quantum Computing: From Concepts to Experiments

    To date, the construction of scalable fault-tolerant quantum computers remains a fundamental scientific and technological challenge, due to the influence of unavoidable noise. In my talk, I will first introduce basic concepts of topological quantum error correction codes, which allow one to protect quantum information during storage and processing. I will discuss recent theory work, perspectives and recent collaborative experimental breakthroughs towards fault-tolerant quantum error correction on various physical quantum computing platforms. This includes the first realisation of repeated high-performance quantum error-correction cycles on a topological surface code with superconducting qubits [1], and the first demonstration of a universal and fault-tolerant logical gate set with trapped ions [2]. Furthermore, I will present new fundamental connections between topological quantum error correction and classical statistical mechanics models, in the context of the correction of qubit loss [3,4] and the determination of fundamental error thresholds for circuit noise [5].

    [1] S. Krinner et al., Realizing repeated quantum error correction in a distance-three surface code, Nature 605, 669 (2022)

    [2] L. Postler et al., Demonstration of fault-tolerant universal quantum gate operations, Nature 605, 675 (2022)

    [3] D. Vodola, et al., Twins Percolation

    [4] R. Stricker et al., Deterministic correction of qubit loss, Nature 585, 207 (2020)

    [5] D. Vodola et al., Fundamental thresholds of realistic quantum error correction circuits from classical spin models, Quantum 6, 618 (2022)


  • (…)


Oct 2023

20 Oct 2023

Workshop on Homotopy Theory and Applications



Jan 2024

M-Theory and Mathematics 2024

on January 15 - 17, 2024

at CQTS @ New York University, Abu Dhabi

Speakers:

Alfonsi\,Giotop. Malek Saemann Minasian Lambert Hull Schreiber He Sati X Han Tan Singh Shahbazi Myers Hohm


Talks:

Talks:






  • 15 Jan 2024

    Eric Sharpe:

    Decomposition of 2D Pure Yang-Mills and the Gross- Taylor String Theory

    slides: pdf

    video: kt

    cf.: arXiv:2307.08729

    In this talk, we will attempt to reconcile two different results on two-dimensional pure Yang-Mills theory. Specifically, we will discuss how the fact that 2d pure Yang-Mills is equivalent to a disjoint union of theories, is related to the Gross-Taylor description of 2d pure Yang-Mills as the target-space field theory of a string theory. The Gross-Taylor picture can be understood by first rewriting the Yang-Mills partition function (in a large N N limit) as a sum of correlation functions in Dijkgraaf-Witten theories for the symmetric group S nS_n, and then interpreting those Dijkgraaf-Witten correlation functions in terms of branched covers, which leads to the string theory description. We first observe that the decomposition of the pure Yang-Mills aligns perfectly with the decomposition of S nS_n Dijkgraaf-Witten theory, and then discuss decomposition and the branched covers interpretation. We encounter two puzzles, and to solve them, propose that the Gross-Taylor string theory has a higher-form symmetry.


  • 16 Jan 2024

    Ruben Minasian:

    Constraining and Un-constraining Supergravities

    slides: pdf

    video: kt

    I will review various aspects and somewhat surprising consequences of cancellation of (different types of) anomalies in supergravity theories in eight and six dimensions. I will also discuss appearance and importance of exotic (singular, non-spin, non-orientable) backgrounds.


  • 16 Jan 2024

    Emanuel Malek:

    Kaluza-Klein Spectrometry for String Theory Compactifications

    slides: pdf

    video: kt

    cf.: arXiv:2212.01135

    I will present a powerful new method that for the first time allows us to compute the Kaluza-Klein spectrum of a large class of string theory compactifications, including those arising in maximal gauged supergravities and beyond. This includes geometries with little to no remaining (super-)symmetries, completely inaccessible by previous methods. I will show how these insights can be used to holographically compute the anomalous dimensions of protected and unprotected operators in strongly-coupled CFTs, as well as to study global properties of their conformal manifolds. I will also show how the method can be used to determine the perturbative stability of non supersymmetric AdS vacua. We will see the importance of higher Kaluza-Klein modes to the physics of string compactifications, e.g. in realising the compactness of moduli spaces, restoring supersymmetry that is lost in a consistent truncation, and in destabilising vacua that appear to stable in lower-dimensional supergravities.


  • 16 Jan 2024

    Fei Han:

    Cubic Forms, Anomaly Cancellation and Modularity

    video: kt

    cf.: arXiv:2005.02344

    Freed and Hopkins developed an algebraic theory of cubic forms, which is an analogy to the theory of quadratic forms in topology. They are motivated by the Witten-Freed-Hopkins anomaly cancellation formula in M-theory, which equals a cubic form arising from an E 8 E_8 bundle over a 12 dimensional spin manifold to the indices of twisted Dirac operators on the manifold. In this talk, we will first review the Witten-Freed-Hopkins anomaly cancellation formula and the algebraic theory of cubic forms, and then show that the cubic forms as well as the anomaly cancellation formula can be naturally derived from modular forms that we construct inspired by the Witten genus and the basic representation of affine 𝔢 8 \mathfrak{e}_8 . Following this approach, we obtain new cubic forms and anomaly cancellation formulas on non-spin manifolds and thus provide a unified way to obtain anomaly cancellation formulas of this type. This is based on our joint work with Prof. Ruizhi Huang, Prof. Kefeng Liu and Prof. Weiping Zhang.




  • 16 Jan 2024

    Christian Saemann:

    Atiyah Algebroids for Higher and Groupoid Gauge Theories

    slides: pdf

    video: kt

    We present an Atiyah algebroid picture for higher and groupoid gauge theories. Common to both is the fact that straightforward definitions of curvatures are only suitable for partially flat cases. Instead, one has to adjust the underlying cocycle relations, leading to new curvatures and gauge transformations. The Atiyah algebroid picture I sketch provides a good idea about the origin of adjustments and why they are required even in the relative conventional case of groupoid gauge theories.


  • 17 Jan 2024

    Chris Hull:

    Self-Dual pp-Form Gauge Fields and the Topology of the Graviton

    slides: pdf

    video: kt

    cf.: arXiv:2307.04748

    Sen’s action for a p p -form gauge field with self-dual field strength coupled to a spacetime metric involves an explicit Minkowski metric and the presence of this raises questions as to whether the action is coordinate independent and whether it can be used on a general spacetime manifold. A natural generalisation of Sen’s action is presented in which the Minkowski metric is replaced by a second metric on spacetime. The theory is covariant and can be formulated on any spacetime. The theory describes a physical sector, consisting of the chiral p p -form gauge field coupled to the dynamical metric gg, plus a shadow sector consisting of a second chiral pp-form and the second metric. The resulting theory is covariant and can be formulated on any spacetime. A spacetime with two metrics has some interesting geometry and some of this is explored here and used in the construction of the interactions. The action has two diffeomorphism-like symmetries, one acting only on the physical sector and one acting only on the shadow sector, with the spacetime diffeomorphism symmetry arising as the diagonal subgroup.



  • 17 Jan 2024 (talk canceled last minute and postponed to 31 Jan)

    Chris Blair:

    Geometry and Dualities of Decoupling Limits in String Theory and M-Theory

    cf.: arXiv:2311.10564

    Our understanding of M-theory is based on a duality web connecting different limits of the theory. I’ll discuss the extension of this duality web to a wide variety of decoupling limits related by duality to the null reduction of M-theory (and hence to the proposal that M-theory can be described by Matrix theory). From a modern perspective, these limits involve non-relativistic geometries, leading to new variants of supergravity in 11- and 10-dimensions. I’ll discuss how to systematically explore these corners of M-theory, following the roadmap of arxiv.org/abs/2311.10564.




Apr 2024


17 April 2024

Workshop: Field Theory and Gravity – Classical and Quantum



19-21 April 2024

Conference: Homotopy Type Theory and Computing – Classical and Quantum

home page: nyuad.nyu.edu/en/events/2024/april/homotopy-type-theory-and-computing.html

live stream: nyu.zoom.us/j/93101580794

The aim of this conference is to discuss Homotopy Type Theory Theory (HoTT) as a substrate for computing and verification in software development, in synthetic homotopy theory, and possibly in application to (topological) quantum computing/simulation.

Some talks will focus on recent progress on the general issue of running HoTT programs, in view of the univalence axiom: such as via “cubical TT” or the more recent “higher observational TT”. Other talks will focus on design patterns for practical (quantum) programming and certification languages, notably via modal types and monadic effects (in modal extensions of HoTT).

In this vein, our local speakers will present a point of contact between modal HoTT and Quantum: the recently developed “Linear HoTT” (LHoTT) that equips classical HoTT with dependentlinear” types which may be thought of as quantum data types. The LHoTT approach to quantum programming interprets a significant fragment of the Proto-Quipper-language, now with identity types enabling full verification.

The conference is to bring this theoretical progress into contact with efforts to use (L)HoTT and related languages like Proto-Quipper for actual (quantum) computing, simulation and verification.

Schedule:

19th20th21st
9:00BuchholtzLeeShulman
10:00MörtbergRileyKovács
11:00LamiauxPaykinRiley
12:00LjungströmFinsterlunch
13:00lunchlunch
14:00WärnGratzer
15:00SchreiberSterling
16:00MyersAltenkirch
17:00RandAngiuli

\,

\;\;\;\;\;\;Paykin \;\;\;\;Wärn \; Myers \;\;\; Kovács \;\;\; Finster \; Schreiber \;\;\;X \;\;\; Altenkirch \; Lamiaux \;Riley \;\;\; Buchholtz \;\;\; Lee

Talks:


May 2024




Quantum Colloquium

Weekly colloquium, broadly on quantum systems, with focus on quantum computation and specifically on topological quantum computation and dependently typed quantum programming languages.


May 2022


Sep 2022





Oct 2022



Nov 2022




  • 21 Nov 2022

    Andrew Kent (Center for Quantum Phenomena, NYU)

    A new spin on magnetism with applications in information processing

    slides: pdf

    video: rec, YT

    Recent advances in magnetism research are likely to have an important impact on electronics and information processing. These advances use the electron magnetic moment (spin) to transmit, write and store information. They enable new devices that operate at high speed with very low energy consumption. The information is stored in the orientation of electron magnetic moments in magnetic materials and can persist without power; energy is only needed to write and read the information. Important physics concepts include the interconversion of electrical (charge) currents into spin currents, the efficiency of the interconversion, controlling the currents, spin polarization direction, and the associated spin torques on magnetic order. Magnetic skyrmions are also of interest both because of their stability — they are topologically protected objects — and because their nucleation and motion can be controlled using spin currents. In this talk I will highlight the new physics concepts that have enabled these advances and discuss some of their applications in information processing.

cf.: J. Appl. Phys. 130 (2021) [doi:10.1063/5.0046950]



Dec 2022


  • 12 Dec 2022

    Leandro Aolita

    Quantum Algorithms, from noisy intermediate scale devices through the early fault-tolerant era

    video: rec, YT

    Reaching long-term maturity in quantum computation science and technology relies on the field delivering practically useful application in a short term. In this colloquium, I will discuss ideas for the noisy intermediate scale (NISQ) and early fault-tolerant eras. I will divide my talk into two parts. In the first part, I will make a brief non-technical introduction to the field, its relevance to the UAE, and the main lines of research of the Quantum Algorithms division at QRC-TII.

    In the second one, I will try to convey some level of technical detail about our work. In particular, I will first present a hybrid classical-quantum algorithm to simulate high-connectivity quantum circuits from low-connectivity ones. This provides a versatile toolbox for both error-mitigation and circuit boosts useful for NISQ computations. Then, I will move on to algorithms for the forthcoming quantum hardware of the early fault-tolerant era: I will present a new generation of high-precision algorithms for simulating quantum imaginary-time evolution (QITE) that are significantly simpler than current schemes based on quantum amplitude amplification (QAA). QITE is central not only to ground-state optimisations but also to partition-function estimation and Gibbs-state sampling, with a plethora of computational applications.


Jan 2023

  • 30 Jan 2023

    Vivek Singh (CQTS @ NYU Abu Dhabi)

    Chern-Simons theory, Knot polynomials & Quivers

    slides: pdf

    video: rec, YT

    cf. arXiv:2103.10228

    First, I will give a brief introduction to knot theory and its connection to Chern-Simons quantum field theory. Then I discuss the method of obtaining polynomial invariants and limitations towards tackling classification of knots. In particular, we will highlight our new results on weaving knots and review the recent developments on Knot-Quiver correspondence.


Feb 2023

  • 13 Feb 2023

    Kazuki Ikeda (Co-design Center for Quantum Advantage, Stony Brook University, USA)

    Demonstration of Quantum Energy Teleportation by Superconducting Quantum Processors and Implications for Communications and High Energy Physics

    Quantum energy teleportation is a theoretical concept in quantum physics that describes the transfer of energy from one location to another without the need for a physical medium to carry it. This is made possible by means of universal properties of quantum entanglement and measurement of quantum states. The role of QET in physics and information engineering is largely unexplored, as the theory has not received much attention for long time since it was proposed about 15 years ago. To validate it on a real quantum processor, my research has tested the energy teleportation protocol in its most visible form for the first time on IBM’s superconducting quantum computer. In my colloquium talk, I will explain the historical background of quantum energy teleportation, quantum circuits and quantum operations. Moreover I will present a concrete setup for a long-distance and large-scale quantum energy teleportation with real quantum networks.

    In addition, I will present the results of quantum simulations with relativistic field theory as a study based on the high-energy physics perspective and the symmetry-protected topological (SPT) phase of matter of quantum energy teleportation. The models will describe include the two dimensional QED (the massive Thirring model), the AKLT model, the Haldane model, and the Kitaev model. Those results show that the phase diagrams of the field theory and SPT phase are closely related to energy teleportation.

    In summary my talk will provide a novel suggestion that quantum energy teleportation paves a new pathway to a link between quantum communication on real quantum network, phase diagram of quantum many-body system, and quantum computation.



  • 27 Feb 2023

    Aeysha Khalique (National University of Science and Technology, Islamabad):

    Computational Tasks through Non-Universal Quantum Computation

    video: YT

    Quantum Mechanics offers phenomena which defy our everyday observation. These are not just theoretical principles but have wide range applications in quantum computation and quantum information, making some tasks possible which are impossible to be done classically. This talk will take you to the journey through quantum computation, starting from underlying principles to the applications, including my own own contribution to it.


Mar 2023


  • 6 Mar 2023

    Altaf Nizamani and Qirat Iqbal (University of Sindh, Pakistan):

    Quantum Technology with Trapped Ions

    video: YT

    Quantum technology is a rapidly advancing field that is poised to revolutionize numerous industries, including computing, communications, sensing, and cryptography. At its core, quantum technology relies on the principles of quantum mechanics, which allow for the creation of devices that operate on the quantum level. These devices based on quantum technology can perform tasks that are impossible or prohibitively difficult for classical devices. One of the most promising applications of quantum technology is in quantum computing, quantum communications, and quantum sensors.

    Trapped ions are one of the promising platform for quantum computing and sensing. In this approach, individual ions are trapped in a vacuum chamber using electromagnetic fields and manipulated using lasers to perform quantum operations. As a quantum system, trapped ions offer several advantages. First, they have long coherence times, meaning that the quantum state of the ion can be preserved for a longer period, allowing for more complex calculations. Second, trapped ions can be precisely controlled and manipulated, allowing for the implementation of high-fidelity quantum gates. Finally, trapped ions can be entangled with one another, allowing for the implementation of quantum algorithms that are impossible to simulate on classical computers. Trapped ions also have great potential as quantum sensors. By using the properties of the ions to measure changes in their environment, trapped ions can detect minute changes in temperature, magnetic fields, and electric fields, among other things. This makes them useful for applications in precision measurement, such as in atomic clocks, gravitational wave detection, and magnetometry.

    One of the major challenges facing trapped ion systems is scalability. While individual ions have been used to perform simple quantum algorithms, scaling the system up to include a large number of ions is a difficult task. However, recent advances in ion trap technology have made it possible to trap larger numbers of ions and transport them in 2D and 3D space to perform more complex operations for quantum computation and sensing experiments. Realization of such devices is not far away. As compared to present atomic clocks, a new generation of quantum-enhanced clocks is now emerging showing significantly improved accuracy. Sensitive physical measurements are an essential component of modern science and technology. Developments in quantum sensors will outdate their classical counterparts.

    We will present recent developments and opportunities in quantum technology applications based on trapped ions, including quantum computation and sensing.


  • 13 Mar 2023

    Roger S. K. Mong (Pittsburgh Quantum Institute, USA)

    Detecting topological order from modular transformations of ground states on the torus

    cf.: arXiv:2203.04329

    Every two-dimensional topological phase is associated with some topological quantum field theory (TQFT), or more formally a modular tensor category. The ground states of a topological phase encode information about the TQFT, which makes them useful in determining the TQFT data, such as anyon mutual statistics and self statistics. For example, many numerical methods for detecting the TQFT relied on the use of minimum entanglement states (MESs), which are the eigenstates of the Wilson loop operators, and are labeled by the anyons corresponding to their eigenvalues. Here we revisit the definition of the Wilson loop operators and MESs. We rederive the modular transformation of the ground states purely from the Wilson loop algebra, and as a result, the modular SS- and TT-matrices naturally show up in the overlap of MESs. Importantly, we show that due to the phase degree of freedom of the Wilson loop operators, the MES-anyon assignment is not unique. This ambiguity means that there are some sets of TQFTs that cannot be distinguished from one another solely by the overlap of MESs.


  • 27 Mar 2023

    Matthias Christandl (Centre for the Mathematics of Quantum Theory, U. Copenhagen):

    Quantum Software

    cf.: arXiv:2009.07161 doi:10.1109/TIT.2022.3169438

    In these days, we are witnessing amazing progress in both the variety and quality of platforms for quantum computation and quantum communication. Since algorithms and communication protocols designed for traditional ‘classical’ hardware do not employ the superposition principle and thus provide no gain even when used on quantum hardware, we are in need of developing specific quantum algorithms and quantum communication protocols that make clever use of the superposition principle and extract a quantum advantage. “Quantum hardware needs quantum software”, so to say. Furthermore, due to noise in the qubits, known as decoherence, an additional quantum-specific software layer is required that emulates a perfect quantum machine on top of a noisy one. I will demonstrate our recent work on this subject with theorems as well data from university and commercial quantum devices.


Apr 2023

  • 3 Apr 2023

    Mouzhe Xie (University of Chicago)

    Diamond-based quantum sensor for molecular analytics

    cf.: arXiv:2108.04843

    slides: pdf

    video: YT

    Quantum sensing technologies enable some of the most precise measurements that human beings have ever achieved. In recent years, optically addressable nitrogen-vacancy (NV) color center hosted by diamond crystal has been used as a novel quantum sensor, which has exquisitely sensitive response to local magnetic field fluctuations. It is therefore capable to perform micro-/nano-scale NMR experiments, manifesting enormous potential to study biological systems on extremely small sample volume – even down to single-molecule regime.

    In this seminar, I will discuss some of the comprehensive efforts to develop NV-based quantum sensing platforms for a wide range of applications in chemistry and biology. I will start with a general introduction to quantum sensing followed by conventional NMR spectroscopy as a powerful tool to study biomolecules, as well as their connections to the NV-based nanoscale NMR. I will then introduce a biocompatible surface functionalization architecture for interfacing a diamond quantum sensor with individual intact biomolecules under physiological conditions. A sensing modality based on diamond membrane integrated with flow channel will also be discussed, which is a promising platform for a variety of experiments a molecular, cellular, and even living-organism levels. Finally, I will conclude by providing an outlook on how NV-based quantum sensing platforms, combined with other advanced spectroscopy and microscopy methods, can be utilized to address important biophysical and bioanalytical questions with unprecedented sensitivity and spatial resolution, which will enhance our understanding of molecular interactions and cellular processes and ultimately improve human health.



  • 10 Apr 2023

    Zain Saleem (Argonne National Lab, USA)

    Classical simulators as quantum error mitigators via circuit cutting

    cf.: arXiv:2212.07335

    video: YT

    We introduce an error mitigation framework that mitigates errors in a quantum circuit using circuit cutting. Our framework can be implemented in polynomial time for a wide variety of quantum circuits. Our technique involves cutting the circuit in such a way that we run the circuit that needs to be executed on the quantum hardware whereas the error mitigation circuit is run on a simulator. We perform error mitigation qubit by qubit and then provide a way to combine the different probabilities from each of the individual qubit error mitigation runs such that the full circuit is error mitigated. We apply our framework to the VQE hardware-efficient ansatz acheiving estimated ground state energies very close to the noise-free simulation results.



  • 24 Apr 2023

    Mauro Paternostro (Queen’s University Belfast, Ireland):

    Alice through the looking glass: cavity optomechanics for the study of the foundation of quantum mechanics

    cf.: arXiv:2302.08995

    I will illustrate how cavity optomechanics is helping us addressing deep questions on our understanding of the foundations of quantum theory, from non-equilibrium quantum dynamics to the collapse of the wave-function. Towards the end of my talk, I will propose an optomechanical pathway for the exploration of the potential quantum nature of gravity.


May 2023


  • 1 May 2023

    Hichem El Euch (American University of Sharjah, UAE):

    High-fidelity universal quantum computation with symmetric qubit clusters

    Designing a physical device that maintains the error rate for each quantum processing operation low is one of the most arduous issues for the implementation of a scalable quantum computer. These errors may result from inaccurate quantum manipulation, such as a gate voltage sweeping in solid-state qubits or a laser pulse duration. Decoherence is usually a manifestation of the interaction with the environment, and it is an entity of the quantum system which generates errors. Small clusters of qubits with symmetries can be used to shield part of them from decoherence. We encode pairs of connected qubits and universal 2-qubit logical gates using 4-level cores with omega-rotation invariance. We show that symmetry renders logical operations particularly resistant to anisotropic qubit rotations that models some quantum errors. We suggest a scalable method for universal quantum processing in which cores act as quansistors, or quantum transistors. By adjusting their intrinsic variables, quansistors may be dynamically isolated from their environment, providing them the adaptability needed to function as controlled quantum memory units.


  • 8 May 2023

    Ilya Kuprov (University of Southampton):

    Optimal control of large spin systems

    cf.: arXiv:2107.00933, arXiv:2303.09458

    video: YT

    In magnetic resonance, optimal control theory is used to generate pulses and pulse sequences that achieve instrumentally difficult objectives (for example, uniform 13C excitation in a 1.2 GHz magnet) with high precision under stringent time and radiofrequency/microwave power constraints. At the moment, the most popular framework is GRAPE (gradient ascent pulse engineering, 10.1016/j.jmr.2004.11.004). This lecture reports our recent mathematical and software engineering work on the various extensions and refinements of the GRAPE framework, and on its implementation as a module of Spinach library. Recently implemented functionality includes: fidelity Hessians and regularised Newton-Raphson optimisation, generalised curvilinear waveform parametrisation, prefix and suffix pulse sequences, multi-target and subspace control, keyhole states and subspaces, cooperative pulses and phase cycles, and piecewise-linear control sequences. In keeping with the long tradition, the methods are also directly applicable to quantum technologies outside Magnetic Resonance.


Sep 2023


Oct 2023

  • 2 Oct 2023

    Titus Neupert (University of Zurich)

    Realizing Higher-Order Topology

    video: Zm

    cf. doi:10.1126/sciadv.aat0346

    Higher-order topology generalizes the bulk-boundary correspondence of topological phases of matter, by allowing topological modes to be localized at corners and hinges instead of edges and surfaces. I will introduce the theory behind this concept, both for noninteracting as well as interacting systems and consecutively discuss two realizations in rather distinct setups. First, as-grown crystals of bismuth, grey arsenic, as well as bismuth bromide are demonstrated to display the essential physics of higher-order topological insulators. Second, it is shown that lattices of so-called Shiba bound states induced by magnetic adatoms in conventional superconductors can be brought into a higher-order superconducting phase. I will report on experimental progress for both system types based on spanning probe as well as transport measurements.



  • 16 Oct 2023

    Anne Broadbent (University of Ottowa, Canada)

    Quantum Delegation with an Off-the-Shelf Device

    video: Zm

    cf. arXiv:2304.03448

    Given that reliable cloud quantum computers are becoming closer to reality, the concept of delegation of quantum computations and its verifiability is of central interest. Many models have been proposed, each with specific strengths and weaknesses. Here, we put forth a new model where the client trusts only its classical processing, makes no computational assumptions, and interacts with a quantum server in a single round. In addition, during a set-up phase, the client specifies the size nn of the computation and receives an untrusted, off-the-shelf (OTS) quantum device that is used to report the outcome of a single constant-sized measurement from a predetermined logarithmic-sized input. In the OTS model, we thus picture that a single quantum server does the bulk of the computations, while the OTS device is used as an untrusted and generic verification device, all in a single round. In this talk, we will show how the delegation of quantum computations can be achieved in the OTS model, and furthermore how to make this protocol zero-knowledge. The emphasis will be on the concepts that contribute to this result; these concepts are drawn from a long line of research related to blind and delegated quantum computation, as well as quantum zero-knowledge proofs. Based on joint work with Arthur Mehta and Yuming Zhao.


  • 23 Oct 2023

    Frank (Peng) Fu (Univ. Soth Carolina):

    Proto-Quipper with Dynamic Lifting

    video: YT, Zm

    Quipper is a functional programming language for quantum computing. Proto-Quipper is a family of languages aiming to provide a formal foundation for Quipper. By virtue of being a circuit description language, Proto-Quipper has two separate runtimes: circuit generation time and circuit execution time. Values that are known at circuit generation time are called parameters, and values that are known at circuit execution time are called states. Dynamic lifting is an operation that enables a state, such as the result of a measurement, to be lifted to a parameter, where it can influence the generation of the next portion of the circuit. As a result, dynamic lifting enables Proto-Quipper programs to interleave classical and quantum computation. In his talk, Dr. Frank will describe how to extend Proto-Quipper-M with dynamic lifting. He will explain the syntax of a language named Proto-Quipper-Dyn. Its type system uses a system of modalities to keep track of the use of dynamic lifting. Then, he will discuss the categorical semantics for dynamic lifting. Finally, if time permits, Dr. Frank will give some examples of Proto-Quipper-Dyn programs.



Nov 2023

  • 06 Nov 2023

    Alberto Marchisio (NYUAD):

    Quantum Machine Learning: Current Trends, Challenges, Opportunities, and the Road Ahead

    video: Zm

    cf. arXiv:2310.10315

    Quantum Computing (QC) claims to improve the efficiency of solving complex problems, compared to classical computing. When QC is applied to Machine Learning (ML) applications, it forms a Quantum Machine Learning (QML) system. After discussing the basic concepts of QC and its advantages over classical computing, this talk reviews the key aspects of QML in a comprehensive manner. We discuss different QML algorithms and their domain applicability, quantum datasets, hardware technologies, software tools, simulators, and applications. Valuable information and resources are provided to jumpstart into the current state-of-the-art techniques in the QML field.


Dec 2023


  • 11 Dec 2023

    Chandrasekhar Ramanathan (Dartmouth College, New Hampshire):

    Quieting Noisy Neighbors: Extending the Coherence Times of Central Electronic Spins in Solids

    video: YT

    cf.: arXiv:arXiv:2311.05396

    Isolated electronic spins such as donors in silicon and defects like the nitrogen-vacancy (NV) center in diamond are promising platforms for some quantum technologies. The decoherence of these spins is often dominated by interactions with other electronic or nuclear spin species present in their vicinity. For example, silicon-29 nuclear spins can limit the coherence times of donors in silicon, and substitutional nitrogen or P1 centers often limit the coherence times of NV centers in diamond. In this talk I will describe two recent sets of experiments from our group where we are able to extend the coherence times of the central spin by engineering these spin-bath interactions. First, I show how the coherence times of phosphorus donors in silicon are influenced by low-power above-bandgap optical excitation. Next, I describe the use of dynamical decoupling techniques to suppress NV-P1 interactions in diamond. In addition to extending coherence times, these decoupling techniques can be used to measure time-dependent magnetic fields, a form of AC-sensing or noise spectroscopy.


Jan 2024


  • 28 Jan 2024

    Alessandra Di Pierro (University of Verona):

    Topological Kernels via Quantum Computation

    cf. arXiv:2307.07383

    Topological data analysis (TDA) enhances the analysis of objects by embedding them into a simplicial complex and extracting useful global properties such as the Betti numbers, i.e. the number of multidimensional holes, which can be used to define kernel methods that are easily integrated with existing machine-learning algorithms. These kernel methods have found broad applications, as they rely on powerful mathematical frameworks which provide theoretical guarantees on their performance. However, the computation of higher-dimensional Betti numbers can be prohibitively expensive on classical hardware, whereas quantum algorithms can approximate them in polynomial time in the instance size. In this work, we propose a quantum approach to defining topological kernels that is based on constructing Betti curves, i.e. topological fingerprint of filtrations with increasing order.


Feb 2024

  • 05 Feb 2024

    Julien Ross:

    Catalytic Embeddings: Theory and Applications

    cf.: arXiv:2305.07720

    video: kt

    Let CC be a quantum circuit and let GG be a set of quantum gates. A catalytic embedding of CC over GG is a pair (D,v)(D,v) consisting of a state vv and a circuit DD over GG such that for every state uu we have D(uv)=(Cu)vD(u \otimes v) = (C u) \otimes v. Because the state vv is left unchanged by the application of DD, it is known as a catalyst. Catalytic embeddings are useful when the circuit CC cannot be exactly represented over the gate set GG. In such cases, one can leverage the catalyst to implement (any number of occurrences of) CC using circuits over GG.

    In this talk, I will present the theory of catalytic embeddings and discuss applications to the exact and approximate synthesis of quantum circuits.


  • 12 Feb 2025

    Chandrashekar Radhakrishnan (NYU Shanghai):

    Theory of Quantum Coherence and Its Application in Quantum Synchronization

    video: Zoom

    Coherence is a well-known feature of quantum systems. An information theoretic investigation of quantum coherence was initiated in [1] from a resource theory perspective. In this talk, I will provide an outline of quantifying coherence, the two different forms corresponding to it namely the intrinsic coherence and local coherence, and trade-off relation between these two types of coherence [2]. As an application, I will talk about the role of quantum coherence in the study of quantum synchronization. First, I will give an overview of synchronization. Then considering an open quantum system comprising of a two-level system interacting with an external environment, I will show how it exhibits phase preference in the long-time limit. While this phase preference, which we identify as quantum phase localization, shows features like Arnold tongue, which is considered as an identifier for quantum synchronization, I present evidence to show that it is not quantum synchronization [3]. Finally, I will discuss the challenges remaining to be addressed in connecting these two related phenomena of quantum phase localization and quantum synchronization.

    References:

    1. T. Baumgratz, M. Cramer, M. B. Plenio, Quantifying Coherence, Phys. Rev. Lett. 113 140401 (2014) [arXiv:1311.0275, doi:10.1103/PhysRevLett.113.140401]
    2. R. Chandrashekar, P. Manikandan, J. Segar, Tim Byrnes, Distribution of quantum coherence in multipartite systems, Phys. Rev. Lett. 116 150504 (2016) [arXiv:1602.00286, doi:10.1103/PhysRevLett.116.150504]
    3. Md. Manirul Ali, Po-Wen Chen, R. Chandrashekar, Physica A 633, 129436 (2024) [doi:10.1016/j.physa.2023.129436]


  • 19 Feb 2024

    Venkata SubbaRao Redrouthu (NYU AD):

    The Quantum Symphony: Electron Spin Choreography for Hyperpolarized Nuclear Spin Sensing

    Delving into the atomic secrets encoded within nuclear spins necessitates a quantum leap in sensitivity. My research endeavors to achieve this leap through Pulsed Dynamic Nuclear Polarization (DNP), an emerging technique that harnesses quantum-controlled electron spins to hyperpolarize nuclear spins, overcoming inherent sensitivity challenges in Nuclear Magnetic Resonance (NMR) spectroscopy.

    In this presentation, I demonstrate a novel quantum mechanical scheme: broad-band pulsed DNP sequences. Comprising carefully choreographed sequences of quantum gates or pulses, each precisely controlled in phase and time, these sequences represent a pivotal advancement beyond conventional DNP methods. Through density matrix-based theoretical analyses and numerical simulations, I navigate the intricacies of these sequences, offering a deeper comprehension of their foundational principles and the quantum symphony they orchestrate in enhancing nuclear spin sensitivity.


  • 26 Feb 2024

    Benoît Valiron:

    Reversible and Quantum Control-Flow

    video: zm, kt

    cf. arXiv:1804.00952

    One perspective on quantum algorithms is that they are classical algorithms having access to a special kind of memory with exotic properties. This perspective suggests that, even in the case of quantum algorithms, the control flow notions of sequencing, conditionals, loops, and recursion are entirely classical. There is, however, another notion of execution control flow that is itself quantum. In this talk, we shall overview the two paradigms and discuss the issues specific to quantum control.


Mar 2024

  • 08 Mar 2024

    Hayder Salman (University of East Anglia):

    Dynamics of a Nonequilibrium Discontinuous Quantum Phase Transition in a Spinor Bose-Einstein Condensate

    cf. arXiv:2312.16555

    video: Zoom

    Symmetry-breaking\;quantum phase transitions lead to the production of topological defects or domain walls in a wide range of physical systems. In second-order transitions, these exhibit universal scaling laws described by the Kibble-Zurek mechanism, but for first-order transitions a similarly universal approach is still lacking. Here we propose a spinor Bose-Einstein condensate as a testbed system where critical scaling behavior in a first-order quantum phase transition can be understood from generic properties. We generalize the Kibble-Zurek mechanism to determine the critical exponents for: (1) the onset of the decay of the metastable state on short times scales, and (2) the number of resulting phase-separated ferromagnetic domains at longer times, as a one-dimensional spin-1 condensate is ramped across a first-order quantum phase transition. The predictions are in excellent agreement with mean-field numerical simulations and provide a paradigm for studying the decay of metastable states in experimentally accessible systems.


  • 25 Mar 2024

    Kapil Kumar:

    Realization and Characterization of Topological Materials

    Topological insulators (TIs) have emerged as a fascinating class of materials with unique electronic properties driven by non-trivial topology. Their exotic behavior, such as robust metallic states on the surface while being insulating in the bulk, has attracted significant attention from both theoretical and experimental communities. Characterizing these materials accurately is crucial for understanding their fundamental properties and exploring potential applications in quantum computing, spintronics, and topological quantum devices.

    This abstract provides an overview of the characterization techniques employed in the study of topological insulators. We discuss both experimental and theoretical approaches utilized to probe their electronic structure, surface states, topological invariants, and transport properties. Experimental techniques encompass a wide range of methods, including angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy/spectroscopy (STM/STS), magneto-transport measurements, and optical spectroscopy. These techniques provide invaluable insights into the band structure, Fermi surface topology, surface states, and the presence of any exotic quantum phenomena.

    On the theoretical front, available various computational methods, such as density functional theory (DFT), tight-binding models, and topological indices, play a pivotal role in predicting and understanding the topological properties of these materials. These theoretical approaches not only aid in interpreting experimental results but also guide the design of novel topological materials with tailored properties.

Apr 2024

  • 15 Apr 2024

    Elisa Ercolessi (University of Bologna, Italy):

    Hybrid Variational Algorithms on a Neutral Atom Platform

    Quantum Computing is seen as a potential breakthrough for the study of hard classical problems as well as for quantum many body systems. However, we are in the era of NISQ devices and still far away from fault-tolerant machines.

    This leads us to consider the possibility of hybrid classical-quantum protocols of variational type: they exploit quantum resources to efficiently prepare states that depend on a suitable chosen set of variational parameters, which can then be determined by means of optimization algorithms to be run on a classical computer. The choice of such classical optimizer schemes is to be guided by compatibility requirements with respect to current available quantum platforms.

    To evaluate the feasibility of such an approach, we present an application of the Quantum Approximate Optimization Algorithm to a typical classical hard combinatorial problem, that has been emulated and tested on a real Rydberg atom quantum machine.

May 2024




Geometry, Topology & Physics (GTP) Seminar

Weekly seminar, broadly on topics in geometry, (algebraic) topology and theoretical/mathematical physics, with focus on applicability to high energy physics/string theory and quantum systems.


Feb 2022


  • 02 Feb 2022

    Luigi Alfonsi (University of Hertfordshire)

    Higher quantum geometry and global string duality

    video: rec

    In this talk I will discuss the relation between higher geometric quantisation and the global geometry underlying string dualities. Higher geometric quantisation is a promising framework that makes quantisation of classical field theories achievable. This can be obtained by quantising either an ordinary prequantum bundle on the ∞-stack of solutions of the equations of motion or a categorified prequantum bundle on a generalised phase space. I will discuss how the higher quantum geometry of string theory underlies the global geometry of T-duality. In particular, I will illustrate how a globally well-defined moduli stack of tensor hierarchies can be constructed and why this is related to a higher gauge theory with the string 2-group. Finally, I will interpret the formalism of Extended Field Theory as an atlas description of the higher quantum geometry of string theory.



Mar 2022


  • 08 March 2022

    David White (Denison University, USA):

    The Kervaire Invariant, multiplicative norms, and N-infinity operads

    video: rec

    In a 2016 Annals paper, Hill, Hopkins, and Ravenel solved the Kervaire Invariant One Problem using tools from equivariant stable homotopy theory. This problem goes back over 60 years, to the days of Milnorand the discovery of exotic smooth structures on spheres. Of particular importance it its solution were equivariant commutative ring spectra and their multiplicative norms. A more thorough investigation of multiplicative norms, using the language of operads, was recently conducted by Blumberg and Hill, though the existence in general of their new “N-infinity” operads was left as a conjecture. In this talk, I will provide an overview of the Kervaire problem and its solution, I will explain where the operads enter the story, and I will prove the Blumberg-Hill conjecture using a new model structure on the categoryof equivariant operads.


  • 16 March 2022

    Guo Chuan Thiang (Beijing University)

    How open space index theory appears in physics

    video: rec

    The incredible stability of quantum Hall systems and topological phases indicates protection by an underlying index theorem. In contrast to Atiyah-Singer theory for compactified problems, what is required is an index theory on noncompact Riemannian manifolds, with interplay between discrete and continuous spectra. Input data comes not from a topological category a la TQFT, but a metrically-coarsened one. This is the subject of coarse geometry and index theory, and I will explain their experimental manifestations.


  • 30 March 2022

    Martin Palmer (Romanian Academy)

    Mapping class group representations via Heisenberg, Schrödinger and Stone-von Neumann

    vido: Zoom

    One of the first interesting representations of the braid groups is the Burau representation. It is the first of the family of Lawrence representations, defined topologically by viewing the braid group as the mapping class group of a punctured disc. Famously, the Burau representation is almost never faithful, but the k=2k = 2 Lawrence representation is always faithful: this is a celebrated theorem of Bigelow and Krammer and implies immediately that braid groups are linear (act faithfully on finite-dimensional vector spaces). Motivated by this, and by the open question of whether mapping class groups are linear, I will describe recent joint work with Christian Blanchet and Awais Shaukat in which we construct analogues of the awrence representations for mapping class groups of compact, orientable surfaces. Tools include twisted Borel-Moore homology of con guration spaces, Schrödinger representations of discrete Heisenberg groups and the Stone-von Neumann theorem.


Apr 2022



  • 13 April 2022

    Mario Velásquez (Universidad Nacional de Colombia)

    The Baum-Connes conjecture for groups and groupoids

    In this talk we present some basics definitions around the Baum-Connes conjecture in the context of groups and groupoids, in particular we define the reduced C *C^\ast-algebra C r *(G)C_r^*(G) of a groupoid G. When a group (or groupoid) satisfies this conjecture we present how we can compute the topological K-theory of C r *(G)C_r^*(G) via a classifying space. We also present some explicit computations and an application about Fredholm boundary conditions in manifolds with corners.


  • 27 April 2022

    Amnon Neeman (Australian National University)

    Bounded t-structures and stability conditions

    We will give a gentle introduction to the topic. We will review the definitions of derived and triangulated categories, of t-structures an of stability conditions. The only new result will come at the very end of the talk, a theorem saying that there are no stability condition on the derived category of bounded complexes of vector bundles on a singular scheme.


May 2022


  • 11 May 2022

    Alex Fok (NYU Shanghai)

    Equivariant twisted KK-theory of noncompact Lie groups

    The Freed-Hopkins-Teleman theorem asserts a canonical link between the equivariant twisted K-theory of a compact Lie group equipped with the conjugation action by itself and the representation theory of its loop group. Motivated by this, we will present results on the equivariant twisted KK-theory of a noncompact semisimple Lie group GG. We will give a geometric description of generators of the equivariant twisted KK-theory of G with equivariant correspondences, which are applied to formulate the geometric quantization of quasi-Hamiltonian manifolds with proper G-actions. We will also show that the Baum-Connes assembly map for the C *C^\ast-algebra of sections of the Dixmier-Douady bundle which realizes the twist is an isomorphism, and discuss a conjecture on representations of the loop group LGL G. This talk is based on joint work with Mathai Varghese.


Sep 2022




Oct 2022

The infinity topos of differentiable sheaves contains all smooth manifolds as a full subcategory and has excellent formal properties. In particular, it admits an intrinsic notion of underlying homotopy type of any differentiable sheaf, which coincides with classical constructions such as taking smooth total singular complexes. Moreover, there is a canonical sense in which the mapping sheaf between any two differentiable sheaves may have the correct homotopy type. This latter notion is reminiscent of the Oka principle in complex geometry. In this talk I will show how to exhibit the Oka principle in the smooth setting using model structures and other homotopical calculi on the infinity topos of differentiable sheaves.




Nov 2022


  • 23 Nov 2022

    Valentino Foit (NYUAD)

    Brownian loops and conformally invariant systems

    slides: pdf

    video: rec, YT

    The Brownian loop soup (BLS) is a stochastic system that is constructed from random loops in the plane and is invariant under conformal transformations. Correlation functions of certain observables can be used to formulate the BLS as a Conformal Field Theory (CFT). I will give an overview of CFTs in two dimensions and point out their relation to certain stochastic systems. Then I will discuss the BLS including some recent progress, such as the operator content, the continuous spectrum, and hints of an extended symmetry algebra.


  • 30 Nov 2022

    Allan Merino,

    Classification and double commutant property for dual pairs in an orthosymplectic Lie supergroup

    video: rec

    One of the main problems in representation theory is to determine the set of equivalence classes of irreducible unitary representations of a Lie group. Using the Weil representation, Roger Howe established a one-to-one correspondence (known as the local theta correspondence) between particular representations of two subgroups GG and GG' forming a dual pair in Sp(W)Sp(W). This correspondence provides a nice way to construct unitary representations of small Gelfand-Kirillov dimension.

    In his wonderful paper “Remarks on classical invariant theory”, Roger Howe suggested that his classical duality should be extendable to superalgebras/supergroups. In a recent work with Hadi Salmasian, we obtained a classification of irreducible reductive dual pairs in a real or complex orthosymplectic Lie supergroup SpO(V)SpO(V). Moreover, we proved a “double commutant theorem” for all dual pairs in a real or complex orthosymplectic Lie supergroup.

    In my talk, I will spend quite some time explaining how the Howe duality works in the symplectic case and then talk about the results we obtained in our paper with H. Salmasian. [arXiv:2208.09746]


Dec 2022

  • 07 Dec 2022

    Emily Riehl (Johns Hopkins University)

    \infty-Category theory for undergraduates

    video: rec, YT

    cf.: arXiv:2302.07855, AMS Notices

    At its current state of the art, \infty -category theory is challenging to explain even to specialists in closely related mathematical areas. Nevertheless, historical experience suggests that in, say, a century’s time, we will routinely teach this material to undergraduates. This talk describes one dream about how this might come about — under the assumption that 22nd century undergraduates have absorbed the background intuitions of homotopy type theory/univalent foundations.



Jan 2023



Feb 2023



  • 22 Feb 2023

    Dmitry Kozlov

    Applied and Computational Topology

    • video: YT

    We will give a brief introduction to the subject of Applied and Computational Topology. The survey of the subject’s main ideas and tools will be complemented with applications to discrete mathematics and to theoretical distributed computing. We will conclude with stating an open problem in combinatorial topology which is related to the complexity of the Weak Symmetry Breaking distributed task.


Mar 2023




Apr 2023





May 2023



Sep 2023




Oct 2023


  • 11 Oct 2023

    Cihan Okay (Bikent University):

    Simplicial Distributions and Contextuality

    video: YT, Zm

    cf. arXiv:2204.06648

    In modern homotopy theory, spaces are represented by combinatorial models called simplicial sets. Their elegant formulation gives them great expressive power to capture spaces up to homotopy. Simplicial distributions are basic mathematical objects that mix simplicial sets with probabilities. That is, they model probability distributions on spaces. In my talk, I will show how simplicial distributions provide a framework for studying a central quantum feature associated with probabilities, known as contextuality. A typical measurement scenario consists of a set of measurements and outcomes, whereas simplicial distributions can be defined for spaces of measurements and outcomes. Our approach unifies and goes beyond two earlier approaches: the sheaf-theoretic (Abramsky-Brandenburger) and group cohomological (Okay-Roberts-Bartlett-Raussendorf).




Nov 2023





Dec 2023



Jan 2024

  • 24 Jan 2024:

    Quentin Ehret:

    Central extensions of restricted Lie superalgebras and classification of pp-nilpotent Lie superalgebras in dimension 4

    video: kt

    cf.: arXiv:2401.08313

    Over a field of positive characteristic pp, restricted Lie algebras are of prime interest, mainly due to their link to algebraic groups and their role in representation theory and classification. The cohomology associated with restricted Lie algebras is considerably more complicated than the ordinary Chevalley-Eilenberg cohomology and explicit formulas are only known up to order 2. In this talk, I will explain how to build the first and second restricted cohomology groups for restricted Lie superalgebras in characteristic pp greater than 3, modifying a previous construction. I will explain how these groups capture some algebraic structures, such as restricted extensions. Further, I will show how to apply this construction to classify pp-nilpotent restricted Lie superalgebras up to dimension 4 over an algebraically closed field of characteristic pp greater than 3. This is a joint work with Sofiane Bouarroudj (NYU Abu Dhabi).


  • 31 Jan 2024

    Chris Blair:

    Geometry and Dualities of Decoupling Limits in String Theory and M-Theory

    cf.: arXiv:2311.10564

    video: zm, kt

    Our understanding of M-theory is based on a duality web connecting different limits of the theory. I’ll discuss the extension of this duality web to a wide variety of decoupling limits related by duality to the null reduction of M-theory (and hence to the proposal that M-theory can be described by Matrix theory). From a modern perspective, these limits involve non-relativistic geometries, leading to new variants of supergravity in 11- and 10-dimensions. I’ll discuss how to systematically explore these corners of M-theory, following the roadmap of arxiv.org/abs/2311.10564.


Feb 2024


  • 14 Feb 2024

    Babak Haghighat (Tsinghua University, China):

    Flat Connections from Irregular Conformal Blocks

    cf. arXiv:2311.13358, arXiv:2311.07960

    video: zm, kt

    I will talk about Liouville conformal blocks with degenerate primaries and one operator in an irregular representation of the Virasoro algebra. Using an algebraic approach, we derive modified BPZ equations satisfied by such blocks and subsequently construct corresponding integral representations based on integration over non-compact Lefschetz cycles. The integral representations are then used to derive novel types of flat connections on the irregular conformal block bundle.


Mar 2024

  • 06 Mar 2024

    Du Pei (Centre for Quantum Mathematics, University of Southern Denmark):

    On New Invariants and Phases of Supersymmetric Quantum Field Theories

    video: Zm, kt

    In this talk, we will explore a novel approach to study supersymmetric quantum field theories using tools from stable homotopy theory. We will explain how this approach leads to new invariants that can be used to detect subtle differences between phases that escape the detection of more conventional invariants.



Apr 2024

  • Alexander Stottmeister (Leibniz Universität Hannover):

    Embezzlement of entanglement and the classification of von Neumann algebras

    cf.: arXiv:2401.07299

    We discuss the embezzlement of entanglement in the setting of von Neumann algebras and its relation to the classification of the latter. Embezzlement (of entanglement), introduced by van Dam and Hayden, denotes the task of producing any entangled state to arbitrary precision from a shared entangled resource state, the embezzling state, using local operations without communication while perturbing the resource arbitrarily little.

    We show that Connes’ classification of type III von Neumann algebras can be given a quantitative operational interpretation in terms of embezzlement. This quantification implies that all type III factors, apart from some type III 0III_0 factors, host embezzling states. In contrast, semifinite factors (type I or II) cannot host embezzling


May 2024



External presentations


Sep 2022


  • 16 Sep 2022 at Math Faculty Meeting, NYU Abu Dhabi

    Urs Schreiber on joint work with Hisham Sati:

    Practical Foundations for Topological Quantum Programming

    slides: pdf


Nov 2022


Dec 2022


Jan 2023




Feb 2023



Mar 2023

Asif Equbal (far left) and Amaria Javed (far right)


Apr 2023

  • 10 Apr 2023

    David Jaz Myers:

    How do you identify one thing with another? – an intro to Homotopy Type Theory

    talk at Prof. Sadok Kallel‘s colloquium,

    American University of Sharjah

    slides: pdf



Aug 2023


Feb 2024







Members

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category: reference

Last revised on May 21, 2024 at 11:57:53. See the history of this page for a list of all contributions to it.