Western Hemisphere Colloquium on Geometry and Physics (WHCGP)

This biweekly online colloquium features geometers and physicists presenting current research on a wide range of topics in the interface of the two fields. The talks are aimed at a broad audience. They will take place via Zoom on alternate Mondays at 3pm Eastern, noon Pacific, 4pm BRT. Each session features a 60 minute talk, followed by 15 minutes for questions and discussion. You may join the meeting 15 minutes in advance. Questions and comments may be submitted to the moderator via the chat interface during the talk, or presented in person during the Q&A session. These colloquia will be recorded and will be available (linked from here) asap after the event.

As an alternative to Zoom, you may watch a live stream of the lecture at: https://youtu.be/48BSjfAYk6o

To receive announcements about the colloquia (including Zoom links to individual meetings), sign up for the WHCGP mailing list here.

Organizing committee: Tudor Dimofte, Ron Donagi, Dan Freed, Sheldon Katz, Dave Morrison, Andy Neitzke.

April 13, 2020

Edward Witten (IAS)

Volumes and Random Matrices

Abstract: I will describe recent results relating two-dimensional gravity and supergravity; volumes of moduli spaces of Riemann surfaces and super Riemann surfaces; and random matrix ensembles. See https://arxiv.org/abs/1903.11115 by Saad, Shenker, and Stanford; https://arxiv.org/abs/1907.03363 by Stanford and me.

Video of lecture OR Video of lecture (alternate version, same content as the other)

Slides of lecture

April 27, 2020

Kevin Costello (Perimeter Institute)

Topological strings, twistors, and Skyrmions

Abstract: It has long been known that holomorphic field theories on twistor space lead to "physical" field theories on Minkowski space. In this talk I will discuss a type I (unoriented) version of the topological B model on twistor space. The corresponding theory on Minkowski space is a sigma-model with target the group SO(8). This is a variant of the Skyrme model that appears as the low-energy effective theory of mesons in QCD. (The group SO(8) appears because of the Green-Schwarz mechanism in the topological string). The origin of this model in the topological string implies many remarkable properties. For one thing, the model is, in a certain sense, integrable. Further, although the Lagrangian is power-counting non-renormalizable, counter-terms at all loops can be uniquely fixed.

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Slides of lecture

May 11, 2020

Mark Gross (Cambridge)

Intrinsic Mirror Symmetry

Abstract: I will talk about joint work with Bernd Siebert, proposing a general mirror construction for log Calabi-Yau pairs, i.e., a pair (X,D) with D a "maximally degenerate" boundary divisor and K_X+D=0, and for maximally unipotent degenerations of Calabi-Yau manifolds. We accomplish this by constructing the coordinate ring or homogeneous coordinate ring respectively in the two cases, using certain kinds of Gromov-Witten invariants we call "punctured invariants", developed jointly with Abramovich and Chen.

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Notes written during lecture

May 18, 2020

Miranda Cheng (Univ. of Amsterdam/National Taiwan University)

Quantum Modularity from 3-Manifolds

Abstract: Quantum modular forms are functions on rational numbers that have rather mysterious weak modular properties. Mock modular forms and false theta functions are examples of holomorphic functions on the upper-half plane which lead to quantum modular forms. Inspired by the 3d-3d correspondence in string theory, a new topological invariants named homological blocks for (in particular plumbed) three-manifolds have been proposed a few years ago. My talk aims to explain the recent observations on the quantum modular properties of the homological blocks, as well as the relation to logarithmic vertex algebras. The talk will be based on a series of work in collaboration with Sungbong Chun, Boris Feigin, Francesca Ferrari, Sergei Gukov, Sarah Harrison, and Gabriele Sgroi.

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Slides of Lecture

June 1, 2020

Davide Gaiotto (Perimeter Institute)

Integrable Kondo problems and affine Geometric Langlands

Abstract: I will present some work on integrable line defects in WZW models and their relation to 4d CS theory, the IM/ODe correspondence and affine generalizations of Geometric Langlands constructions.

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June 15, 2020

Maxim Kontsevich (IHES)

Space-time analyticity in QFT

Abstact: I will talk on a joint work with Graeme Segal. We propose a new axiomatics for unitary quantum field theory which includes both Lorentzian and Euclidean signatures for curved space-time manifolds. The key to the definition is certain open domain in the space of complex-valued symmetric bilinear forms on a real vector space. The justification comes from holomorphic convexity (lower bound) and from higher gauge theories (upper bound).

June 22, 2020

Anton Kapustin (Cal Tech)

June 29, 2020

Sakura Schafer-Nameki (Oxford)

July 6, 2020

Nima Arkani-Hamed (IAS)

July 13, 2020

Mina Aganagic (UC Berkeley)

July 20, 2020

Greg Moore (Rutgers)

July 27, 2020

Laura Fredrickson (Stanford/U. Oregon)

August 3, 2020

TBA

August 10, 2020

TBA

August 17, 2020

TBA

August 24, 2020

TBA