Alejandro Poveda

Speaker: Xin Guo, UC Berkeley Title: Generative Adversarial Networks (GANs): An Analytical Perspective Abstract: Generative models have attracted intense interests recently. In this talk, I will discuss one class of generative models, Generative Adversarial Networks (GANs).  I will first provide a gentle review of the mathematical framework behind GANs. I will then proceed to discuss a few […]

Speaker: Yu-Shen Lin (Boston University) Title: Gravitational Instantons Abstract: Gravitational instantons were introduced by Hawking as building blocks of his Euclidean quantum gravity theory back in the 1970s. These are non-compact Calabi-Yau surfaces with L2 curvature and thus can be viewed as the non-compact analogue of K3 surfaces. K3 surfaces are 2-dimensional Calabi-Yau manifolds and […]

Speaker: Joel D. Hamkins (Notre Dame and Oxford) Title: An exploration of infinite games—infinite Wordle and the Mastermind numbers Abstract: Let us explore the nature of strategic reasoning in infinite games, focusing on the cases of infinite Wordle and infinite Mastermind. The familiar game of Wordle extends naturally to longer words or even infinite words in an […]

Speaker: Boaz Barak (Harvard) Title: On Provable Copyright Protection for Generative Model Abstract: There is a growing concern that learned conditional generative models may output samples that are substantially similar to some copyrighted data C that was in their training set. We give a formal definition of near access-freeness (NAF) and prove bounds on the probability that a […]

Speaker: Manuel Cortés-Izurdiaga (University of Malaga) Title:  Homotopy categories of rings: some properties and consequences in module categories Abstract: Given a non-necessarily commutative ring with unit and an additive subcategory of the category of right modules, one can consider complexes of modules in the subcategory and the corresponding homotopy category. Sometimes, these homotopy categories are the […]

Speaker: Matthew Foreman (UC Irvine) Title: Impossibility results in classical dynamical systems Abstract: In 1932, motivated by questions in statistical and celestial mechanics, von Neumann proposed classifying the statistical behavior of dynamical systems. In the 1960's, motivated by work of Poincaré, Smale proposed classifying the qualitative behavior of dynamical systems.  These questions laid the groundwork for enormous amounts of work, but […]

Speaker: Brian Williams (Boston University) Title: Koszul duality in QFT Abstract: We will describe appearances of the algebraic phenomena of Koszul duality in the context of boundary conditions and defects in quantum field theory. Primarily motivated by topological string theory, this point of view was pioneered by Costello and Li in their proposal for a […]

Speaker: Jeff W. Lichtman (Harvard University) Title: The analytical challenges of connectomics Abstract: Recent progress in generating synapse-level maps of brains, a field known as connectomics, brings both opportunities and challenges. The upside is that the biophysical instantiation of memories, behaviors, and knowledge will soon be before us. The downside is that no one knows exactly how […]

Speaker: Dana Bartosova (University of Florida) Title: What do topological dynamics, combinatorics, and model theory have in common? Abstract: A striking correspondence between dynamics of automorphism groups of countable first order structures and Ramsey theory of finitary approximation of the structures was established in 2005 by Kechris, Pestov, and Todocevic. Since then, their work has been generalized […]

Speaker: Xuwen Zhu (Northeastern) Title: Analysis of ALH* gravitational instantons Abstract: Gravitational instantons are non-compact Calabi-Yau metrics with L^2 bounded curvature and are categorized into six types. We will discuss one such type called ALH* metrics which has a non-compact end modelled by the Calabi ansatz with inhomogeneous collapsing near infinity. Such metrics appeared recently in the works on SYZ conjecture, […]

Colloquium Speaker: Justin Moore (Cornell University) Title: Homology, higher derived limits, and set theory Abstract: Singular homology has a number of well-known defects when used to study spaces such as the Hawaiian earring and solenoids. It may not reflect the "shape" of the space and can give counterintuitive information about its dimension. One remedy of […]