Date/Time : 09 Apr 2024 17:00
Venue : S17 #05-11 (SR5)
Speaker : Piotr Kowalski, The University of Wrocław

I plan to discuss the notions of model companion and model completeness focusing on algebraic and geometric examples. For instance, I will mention recent joint work with Daniel Max Hoffmann, Chieu-Minh Tran and Jinhe Ye, where we consider model completeness of certain matrix group.

Add to calendar :

Date/Time : 08 Apr 2024 14:00
Venue : S17 #04-05 (SR2)
Speaker : Chris Leininger, Rice University

A billiard trajectory in a polygon in the Euclidean or hyperbolic plane is the path of a particle in the polygon, following a geodesic line until it hits the side, reflects off, and continues. This trajectory gives rise to a symbolic coding, its “bounce sequence”, which is (generically) a biinfinite sequence recording the sides encountered (which we assume are labeled). In joint work with Erlandsson, Duchin, and Sadanand, we prove that generically the “bounce spectrum” (i.e. the set of all bounce sequences of biinfinite trajectories), determines the shape of the polygon. The “non-generic” case is also understood, and we can completely determine when two polygons have the same bounce spectrum. In the talk, I’ll explain this theorem and describe how it is related to non-positively curved cone metrics on surfaces.

Add to calendar :

Date/Time : 03 Apr 2024 15:00
Venue : S17 #04-06 (SR1)
Speaker : Tomoyuki Arakawa, Kyoto University

The 4D/2D duality is a physical theory discovered rather recently by Beem et al, which gives a vertex algebra to any 4D N=2 superconformal field theory. The resulting vertex algebra is an important invariant of a 4-dimensional theory, which may be regarded as a refinement of the Higgs branch.

In this talk I will discuss the representation theory of vertex algebras arising from 4-dimensional theories.

Add to calendar :

Date/Time : 03 Apr 2024 16:30
Venue : S17 #04-06 (SR1)
Speaker : Xuanzhong Dai, RIMS, Kyoto University

It has been suspected for a long time that the Rankin-Cohen brackets of modular forms should be related to vertex operator algebras as initially suggested by W. Eholzer, Y. Manin and D. Zagier. Our attempt involves sheaf constructions known as the chiral de Rham complex, whose cohomology is linked to the Witten genus. For arbitrary congruence subgroup of modular group, the fractional linear transformation induces an action on the global section of chiral de Rham complex on the upper half plane. We consider the invariant sections under the action of the congruence subgroups with suitable cuspidal conditions. It is noteworthy that modular forms appear naturally on invariant sections.

Add to calendar :

Date/Time : 03 Apr 2024 15:30
Venue : S17 #05-12 (SR4)
Speaker : DO Thai Duong, National University of Singapore

We will present some properties of the higher complex Sobolev spaces. These spaces share several similar properties with the complex Sobolev space; in particular, we can build their corresponding Vigny’s functional capacity and prove the Moser-Trudinger inequality for these spaces. We also discuss the relation of these spaces with the complex Monge-Ampere equation. This talk is based on my joint work with Nguyen Duc-Bao.

Add to calendar :

Date/Time : 27 Mar 2024 16:00
Venue : S17 #04-05 (SR2)
Speaker : Xiaochuan Tian, University of California, San Diego

Meshfree and particle methods are widely used in computational studies of partial differential equations, offering many advantages compared to traditional mesh- or grid-based numerical methods. Nevertheless, many practical questions revolve around meshfree methods, encompassing concerns about stability and accuracy. We propose a new paradigm of designing meshfree methods for solving partial differential equations (PDEs) through nonlocal analysis, inspired by the recent development of nonlocal calculus and its applications. We propose that the development of stable, accurate, and efficient meshfree methods relies on two key factors: (1) the formulation of well-posed continuum nonlocal models to approximate the PDE models and (2) the development of asymptotically compatible schemes for robust discretization of nonlocal models that allow a flexible coupling of the modeling and discretization parameters. We will review several aspects of nonlocal calculus and asymptotically compatible schemes and demonstrate the idea with a monotone meshfree method for solving linear elliptic equations in non-divergence form.

Add to calendar :

Date/Time : 27 Mar 2024 14:30
Venue : S17 #05-12 (SR4)
Speaker : Wu Hao, National University of Singapore

Let X be a compact Riemann surface and L be a positive line bundle on it. We study the conditional zero expectation of all the holomorphic sections of L^n which do not vanish on D for some fixed open subset D of X. We prove that as n tends to infinity, the zeros of these sections are equidistributed outside D with respect to some probability measure. This gives rise to a surprising forbidden set.

Add to calendar :

Date/Time : 27 Mar 2024 14:00
Venue : S17 #06-11 (SR6)
Speaker : Shi-Zhuo Looi, California Institute of Technology

We present a framework and algorithm for deriving the sharp asymptotics of linear and non-linear wave equations on asymptotically flat spacetimes with even spatial dimensions, including non-stationary spacetimes without spherical symmetry assumptions.

Add to calendar :

Date/Time : 27 Mar 2024 17:00
Venue : S17 #04-05 (SR2)
Speaker : Kyle Gannon, Peking University

This talk is motivated by the following two soft questions: How do we sample an infinite sequence from a first order structure? What model theoretic properties might hold on almost all sampled sequences? We advance a plausible framework in an attempt to answer these kinds of questions. The central object of this talk is a proability space. The underlying set of our space is a standard model theoretic object, namely the space of types in countably many variables over a monster model. Our probability measure is an iterated Morley product of a fixed Borel-definable Keisler measure. Choosing a point randomly in this space with respect to our distribution yields a random generic type in infinitely many variables. We are interested in which model theoretic events hold for almost all random generic types. Two different kinds of events will be discussed: (1) The event that the induced structure on a random generic type is isomorphic to a fixed structure; (2) the event that a random generic type witnesses a dividing line. This work is joint with James Hanson.

Add to calendar :