nLab
Math-Phys-Cat

Math-Phys-Cat is a Brazilian research group concerned with Mathematical-Physics, categorification and higher category theory and physics. We are mainly interested in mathematical aspects of classical and quantum field theories, especially those involving category theory and gauge theory, also in the axiomatization problem of astrophysics and in using category-theoretic language in order to unify and abstract concepts in classical algebra and in differential geometry.

• Website: math-phys.group.

• On the birth of the group: Mathematical Physics or Mathematical-Physics?.

• We also have a blog, where we write about our works. There you will also find a column, called This Quarterly Finds on Math-Phys-Cat Group in honor to Baez’s seminal This Week’s Finds on Mathematical Physics, where quarterly we present what our group has been doing.

• You can also find us on: Twitter, arXiv, Researchgate, mathoverflow, ORCID, Zenodo, etc.

Contact

• The best way to contact us is through the email [e-mail].

• We also have a Zulipchat. If would like to join us, please, contact us.

Activies

• Since it was created, our group has been offered courses, minicourses and a lot of student seminars (a weekly seminar where the students present his studies). See here. For some of them a detailed schedule and lecture notes are available.

• We started online Group Seminars, weekly seminars, where in each week a different member present something related with his work. External speakers are welcome. If you are interested, please, contact us.

• For the schedule and slides, see here;

• For video recordings, see our Youtube Channel. Currently it is being update every Wednesday, after the seminars.

Current Members

See also here. We are fully open for new members and new interactions. If you are interested, please, contact us.

Professors

• Rodney Josué Biezuner (Math-UFMG)
• Fábio Dadam (Math-UTFPR)
• Helvécio Geovani Fargnoli Filho (Math-UFLA)
• Maurício Corrêa (Math-UFMG)
• Elizaveta Vishnyakova (Math-UFMG)
• Hassan Najafi Alishah (Math-UFMG)
• Raphael Campos Drumond (Math-UFMG)
• Fernando Pereira Paulucio Reis (Math-UFES)
• Maico Felipe Silva Ribeiro (Math-UFES)

Independent Researchers

• Leonardo Lopes Abath (Brazil)
• Fereshteh Bahadorykhalily (Iran)

PhD Students

• Yuri Ximenes Martins (Math-UFMG)
• Rodrigo de Castro Lima (Phys-UNESP)

MSc Students

• Daniel de Souza Plácido Teixeira (Math-UFMG)
• Luiz Felipe Andrade Campos (Math-UFMG)
• Mayk Alves de Andrade (Math-UFMG)
• Pedro Brunialti Lima de Andrade (Math-UFMG)

Undergrad Students

• Cyro Barros Murgulo (Phys-UFMG)
• Bryant Rosado Silva (Math-UFMG)
• Douglas Vilela de Paiva Silva (Phys-UFMG)

Research Topics

For a selected list of publications, see here. For the list of members involved in each topic, see our website.

Gauge Theory

• algebra-valued gauge theories;

• obstruction theory applied to gauge theories;

• mathematical dualities between gauge theories;

• extensions of gauge theories;

• higher gauge theory.

General Aspects of Field Theories

• emergence theory for Lagrangian field theories;

• classification methods on gravity theories;

• topological and geometric investigations in superstring theory.

Quantum Field Theory and Quantum Gravity

• quantum dualities and anomalies in perturbative gauge theories;

• investigations in loop quantum gravity;

• quantum field theory in curved spaces.

Mathematical Foundations of Quantum Mechanics

• many-body systems;

• quantum information and quantum comunication;

• quantum coherence and entanglement;

• open systems and reduced dynamics.

Differential Geometry

• regularity theory in structured manifolds and others smooth spaces;

• general theory of graded and supermanifolds;

• localization theory on complex supermanifolds;

• holomorphic Poisson geometry;

• geometry of co-Higgs Sheaves;

• general symplectic geometry and Dirac manifolds

• Hamiltonian systems and integrable systems;

• geometric methods in partial differential equations;

• singularity theory (Milnor fibrations, Thom-regularity, etc.)

Algebra and Algebraic Geometry

• superalgebras of vector fields on supermanifolds;

• sheaf-theoretic aspects and cohomology of supermanifolds;

• investigations in noncommutative algebraic geometry

Categorification, Abstraction and Unification

• categorification of standard results in algebra and differential geometry;

• higher algebra and higher geometry;

• categorification of Feynman graphs and Feynman rules

Cosmology and Astrophysics

• axiomatization of stellar systems;

• obstruction theory on Astrophysics;

• elliptic methods on Astrophysics;

• investigations on early Universe;

• dark matter and dark energy;

• quantum cosmology models;

• methods of QFT on curved spaces applied to Cosmology.

Internal Structure

Our group does not receive any outside assistance. Since the process of maintaining, organizing and updating a website and their related social medias requires expensive time, which sometimes is not so recognized, in this page we would like to make explicit these hidden people and their very important work. The following is the current list of people with their corresponding internal concern. It may change over time. It is not displayed in order of importance.

• Yuri Ximenes Martins: admin and owner of the domain math-phys.group

• Mayk Alves de Andrade: translator (notice that our site is also available in Brazilian portuguese)

• Cyro Barros Murgulo: translator

• Bryant Rosado Silva: Twitter (where the news of our group are released)

• Douglas Vilela de Paiva Silva: Academia.edu and Mendeley (repositories where our works are uploaded)

• Pedro Brunialti Lima de Andrade: updater (responsible for collecting new information and doing a quarterly update of the fundamental data of our website)

• Daniel de Souza Plácido Teixeira: creator and organizer of Zulip (where the discussion are being made) and our group seminar.

category: people