# WOMEN AT THE INTERSECTION OF MATHEMATICS AND THEORETICAL PHYSICS

America/Toronto
Perimeter Institute

#### Perimeter Institute

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Description

This (online) meeting aims to create new bridges between mathematics and physics and to strengthen the existing ones, by bringing together women mathematicians and physicists from various horizons working on the border of these two disciplines. It is aimed at identifying new trends of research at the frontier between mathematics, quantum field theory and string theory and exploring how they intertwine.

By essence an interdisciplinary meeting, it is expected to trigger interactions between the senior and junior participants, who will be encouraged to meet up in a mentoring scheme as part of the conference programme. The scientific programme of the meeting will be geared around three transversal topics: Symmetry and Duality, Locality and Singularity, Topological and Geometric Invariants.

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land.

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

Participants
• Abhishek Mathur
• Afreen Naz
• Alaa Almushaikeh
• Alessandra Frabetti
• Alessia Platania
• Ana Ros Camacho
• Annalisa Panati
• Anne Taormina
• Astrid Eichhorn
• Asuka Takatsu
• Bhuvaneswari Surya
• Bianca Dittrich
• Bruce Rout
• Carlos Perez-Sanchez
• Carolina Neira Jimenez
• Caroline Laure Mbakob Tchouawou
• Catherine Meusburger
• Celina Pasiecznik
• Cemile Arabaci
• Chikako Mese
• Clara Winckler
• Clare Dunning
• Claude Roger
• Claudia Malvenuto
• Claudia Rella
• Claudia Scheimbauer
• Colleen Delaney
• Corina Keller
• Cristina Diamantini
• Diana Mendez Avalos
• Doreen Fraser
• Dorothea Bahns
• Eilind Karlsson
• Elise LePage
• Encieh Erfani
• Eugenia Colafranceschi
• Eveliina Peltola
• Evelyn Yoczira Lira Torres
• Fay Dowker
• Fobasso Mbognou Florette Corinne
• Giulia Peveri
• Inderpreet Kaur
• Jennifer Brown
• Julia Pasiecznik
• Juliette Benitez
• Karen Yeats
• Kartikey Sharma
• Kasia Rejzner
• Kimberly Kuntz
• Laura Edmonds
• Laura Elena Gonzalez Bravo
• Laurent Freidel
• Libby Farrell
• Lisa Glaser
• Lisa Morhaim
• Lissa de Souza Campos
• Luiza Mayara Santos Miranda
• Maajida Murdock
• Mahumm Ghaffar
• Maite Dupuis
• Manasa Manjunatha
• Maria Elena Tejeda-Yeomans
• Maryam Khaqan
• Maryam Qaiser
• Masoumeh Tavakoli
• Nafisa Raihana
• Nathan Lombard
• Nichol (Cohl) Furey
• Nicolas Delporte
• Nina Holden
• Nomaan X
• Nor Anita Rezle
• Oindrila Ghosh
• Philine van Vliet
• Qiaoyin Pan
• Reiko Toriumi
• Renate Loll
• Roberta Iseppi
• Roukaya Dekhil
• Sabine Harribey
• Sam Crawford
• Samiha Ali
• Sana Tabaza
• Sanghamitra Vijay Anand
• Sarah Rourke
• Shan Liu
• Shannon Jeffries
• Sharmila Gunasekaran
• Sree Ram Valluri
• Srishti Nautiyal
• Stav Zalel
• Sumati Surya
• Susama Agarwala
• Sylvie Paycha
• Theo Johnson-Freyd
• Valentina Forini
• Vera Maiboroda
• Viviane Fairbank
• Yue Sun
Stephanie Mohl
• Monday, 22 February
• 09:50 10:00
Welcome and Opening Remarks 10m
Speakers: Anne Taormina (Durham University), Bianca Dittrich (Perimeter Institute), Katarzyna Rejzner (University of York), Reiko Toriumi (Okinawa Institute of Science and Technology), Sylvie Paycha (University of Potsdam), Theo Johnson-Freyd (Perimeter Institute)
• 10:00 10:25
Division algebraic symmetry breaking 25m

Can the 32C-dimensional algebra RCHO offer anything new for particle physics? Indeed it can. Here we identify a sequence of complex structures within RCHO which sets in motion a cascade of breaking symmetries: Spin(10) -> Pati-Salam -> Left-Right symmetric -> Standard model + B-L (both pre- and post-Higgs-mechanism). These complex structures derive from the octonions, then from the quaternions, then from the complex numbers. It should be noted that this pattern would not have been obvious within the standard formalism.

Speaker: Nichol Furey (Humboldt University of Berlin)
• 10:25 10:30
Break 5m
• 10:30 10:55
State sum models with defects 25m

"We explain how to construct a Turaev-Viro state sum model with defect planes, defect lines and defect points. This is work in progress with John Barrett."

Speaker: Catherine Meusburger (University of Erlangen-Nürnberg)
• 10:55 11:00
Break 5m
• 11:00 11:25
Quantum information and black holes 25m

"The concepts of quantum information theory play an important role in two seemingly distinct areas of physics: For studying the quantum properties of black holes as well as for devising quantum computing algorithms. Quantum entanglement and computational complexity may be mapped to  geometric quantities. This is intimately related to the holographic principle, according to which the information stored in a volume is encoded on its surface, as is the case for black holes.  In the talk I will describe the essential new concepts that relate quantum information to geometry and gravity. Technically, this involves generalising quantum information results to quantum field theories, i.e. from finite to infinite-dimensional Hilbert spaces. I will explain how the new  relations may be used to obtain both a further
understanding of quantum black holes, as well as further advances for the theoretical foundations of quantum computing."

Speaker: Johanna Erdmenger (Julius-Maximilians-Universität Würzburg)
• 11:25 11:30
Break 5m
• 11:30 12:30
Discussion Session: Symmetry and Duality
• 12:30 13:15
Break via Remo 45m
• 13:15 14:15
Researcher Presentations
• Tuesday, 23 February
• 09:00 10:00
Mentoring Sessions
• 10:00 10:25
Mathematical Puzzles from Causal Set Quantum Gravity 25m

I will discuss some of the mathematical puzzles that arise from the causal set approach to quantum gravity. In this approach, any causal continuum spacetime is said to be emergent from an underlying ensemble of locally finite posets which represents a discretisation of the causal structure. If the discrete substructure is to capture continuum geometry to sufficient accuracy, then it must be "approximately" close to it. How can we quantify this closeness? This discreteness, while also preserving local Lorentz invariance, leads to a fundamental non-locality. This is not only an obstacle to a “traditional” initial value formulation, but also to the geometric interpretation of entanglement entropy. Is there an analytic way to quantify the remanent Planckian non-locality? These questions, as well as others arising from the quantum dynamics of causal, may be of potential interest to mathematicians, in particular Geometers and Combinatorists.

Speaker: Sumati Surya (Raman Research Institute)
• 10:25 10:30
Break 5m
• 10:30 10:55
On generalized hyperpolygons 25m

In this talk we will introduce generalized hyperpolygons, which arise as Nakajima-type representations of a comet-shaped quiver, following recent work joint with Steven Rayan. After showing how to identify these representations with pairs of polygons, we shall associate to the data an explicit meromorphic Higgs bundle on a genus-g Riemann surface, where g is the number of loops in the comet. We shall see that, under certain assumptions on flag types, the moduli space of generalized hyperpolygons admits the structure of a completely integrable Hamiltonian system.

Speaker: Laura Schaposnik (University of Illinois at Chicago)
• 10:55 11:00
Break 5m
• 11:00 11:25
Exploring spacetime beyond classicality 25m

The physics of General Relativity is deeply intertwined with the mathematics of Lorentzian differentiable manifolds. The latter provide excellent models of spacetime across a vast range of physical scales, encoding gravitational interactions into the curvature properties of smooth metric spaces. However, describing geometry in terms of the infinitesimal line element "ds" does not seem appropriate in the quantum regime near the Planck scale. -- Coming from different perspectives, geometers, classical relativists and quantum gravity researchers are actively investigating more general geometric settings, abandoning smoothness or even continuity of the metric space. The crucial question is what aspects of standard (pseudo-)Riemannian geometry survive, and what this tells us about the "essence" of curvature and geometry and about the ultimate nature of physical spacetime. Can we learn from each others' insights?

Speaker: Renate Loll (Radboud University Nijmegen)
• 11:25 11:30
Break 5m
• 11:30 12:30
Discussion Session: Locality and singularity
• 12:30 13:15
Break via Remo 45m
• 13:15 14:15
Researcher Presentations
• 14:15 15:15
Mentoring Sessions
• Wednesday, 24 February
• 09:00 10:00
Mentoring Sessions
• 10:00 10:25
A gentle introduction to (modular tensor) categories 25m

In this talk we will introduce categories, a notion that packages mathematical objects of any kind and provides an abstract language to study them. We will build up our way towards so-called modular tensor categories, which roughly speaking are categories with a tensor product, duals, and quite a bit of extra categorical structure. They arise in (rational) conformal field theory and its study poses many interesting questions on their classification, internal structure and generalizations. I will give an overview of these questions and some current lines of research in this topic.

Speaker: Ana Ros Camacho (Cardiff University)
• 10:25 10:30
Break 5m
• 10:30 10:55
Speaker: Valentina Forini (City University of London)
• 10:55 11:00
Break 5m
• 11:00 11:25
From gauge fields to direct connections on gauge groupoids 25m

"Geometrically, a gauge theory consists of a spinor bundle describing the matter fields, associated to some principal bundle whose gauge group rules the internal symmetries of the system. The gauge fields are the local expressions of a principal connection inducing a covariant derivative which settles the dynamics of the matter fields.
Principal connections can be seen as parallel displacements on the fibres of the principal bundle along curves on the base manifold. In this talk I shortly present a generalisation of gauge fields given by direct connections on gauge groupoids, based on a work in progress with S. Azzali, Y. Boutaib, A. Garmendia and S. Paycha."

Speaker: Alessandra Frabetti (Université Claude Bernard Lyon 1)
• 11:25 11:30
Break 5m
• 11:30 12:30
Discussion Session: Topological and geometric invariants
• 12:30 13:00
Break via Remo 30m
• 13:00 14:15
Why women leave: Model women and models of discrimination 1h 15m

"In this talk, I posit two concepts from the economics literature as hypotheses for the observed data on women in academia. This talk includes time for discussion about how these concepts can inform our approach to mentoring junior women.
"

Speaker: Susama Agarwala (Johns Hopkins University )
• 14:15 15:15
Mentoring Sessions
• Thursday, 25 February
• 09:00 10:00
Mentoring Sessions
• 10:00 10:25
Change the coefficients of conditional entropies in extensivity 25m

The Boltzmann--Gibbs entropy is a functional on the space of probability measures. One characterization of the Boltzmann--Gibbs entropy is given by the Shannon--Khinchin axioms, which consist of continuity, maximality, expandability and extensivity. The extensivity is expressed in terms of the linear combinations of conditional probabilities. Replacing the coefficients in the linear combinations with a power function provides a characterization of the Tsallis entropy. I talk about the impossibility to replace the coefficients with a non-power function.

Speaker: Asuka Takatsu (Tokyo Metropolitan University)
• 10:25 10:30
Break 5m
• 10:30 10:55
On hidden quantum group symmetries in CFT 25m

"I discuss applications of a hidden $U_q(\mathfrak{sl}_2)$-symmetry in CFT with central charge $c \leq 1$ (focusing on the generic, semisimple case, with $c$ irrational). This symmetry provides a systematic method for solving Belavin-Polyakov-Zamolodchikov PDE systems, and in particular for explicit calculation of the asymptotics and monodromy properties of the solutions. Using a quantum Schur-Weyl duality, one can understand solution spaces of such PDE systems in a detailed way. The solutions, in turn, are useful both for CFT questions and for rigorous understanding of the connections of 2D CFT with critical models of statistical physics."

Speaker: Eveliina Peltola (Bonn University)
• 10:55 11:00
Break 5m
• 11:00 11:25
Entropy and energy fluctuations in non-equilibrium quantum statistical mechanics 25m

"Non-equilibrium statistical mechanics has seen some impressive developments in the last three decades, thank to the pioneering works of Evans, Cohen, Morris and Searles on the violation of the second law, soon followed by the ground-breaking formulation of the Fluctuation Theorem by Gallavotti and Cohen for entropy fluctuation in the early nineties. Their work was by vast literature, both theoretical and experimental

The extension of these results to the quantum setting has turned out to be surprisingly challenging and it is still an undergoing effort. Kurchan’s seminal work (2000) showed the measurement role has to be taken in account, leading to the introduction of the so called two-time measurement statistics (also known as full counting statistics). However in this context, the lack of a trajectory notion leads to both conceptual and technical problems, or phenomena with no classical counterpart, as underlined by some of our recent results.

In this talk I will review some of the key concept involved in the Fluctuation Theorem and its extensions to the quantum setting; I will present some recent results exploring the role played by ultraviolet regularity conditions (joint work with R.Raquépas and T.Benoist )."

Speaker: Annalisa Panati (University of Toulon)
• 11:25 11:30
Break 5m
• 11:30 12:30
Discussion Session: Gender
• 12:30 13:15
Break via Remo 45m
• 13:15 14:15
Poster Presentations & Good-Bye
• 14:15 15:15
Mentoring Sessions