Interdisciplinary Science Seminar Speaker: Yinbang Lin (Tongji University) Title: Moduli spaces of stable pairs on algebraic surfaces Abstract: As a variant of Grothendieck’s Quot schemes, we introduce the moduli space of limit stable pairs. We show an example over a smooth projective algebraic surface where there is a virtual fundamental class. We are able to […]
Nathanan Tantivasadakarn (Harvard) Video Title: Hybrid Fracton Orders Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”. First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to […]
Sergiu Klainerman (Princeton University) Title: Nonlinear stability of Kerr black holes for small angular momentum Abstract: According to a well-known conjecture, initial data sets, for the Einstein vacuum equations, sufficiently close to a Kerr solution with parameters $a, m$, $|a|/m <1$, have maximal developments with complete future null infinity and with domain of outer communication (i.e complement of […]
This workshop will take place May 7-9 (Friday-Sunday), 2021 virtually on Zoom The aim of the workshop is to bring together a community of researchers in mathematics, computer science, and data science who develop theoretical and computational models to characterize shapes and analysis of image data. This workshop is part of the NSF FRG project: […]
Frances Kirwan (University of Oxford) Title: Moment maps and the Yang-Mills functional Abstract: In the early 1980s Michael Atiyah and Raoul Bott wrote two influential papers, ‘The Yang-Mills equations over Riemann surfaces’ and ‘The moment map and equivariant cohomology’, bringing together ideas ranging from algebraic and symplectic geometry through algebraic topology to mathematical physics and number theory. […]
Amit Sahai (UCLA) Title: Indistinguishability Obfuscation: How to Hide Secrets within Software Abstract: At least since the initial public proposal of public-key cryptography based on computational hardness conjectures (Diffie and Hellman, 1976), cryptographers have contemplated the possibility of a “one-way compiler” that translates computer programs into “incomprehensible” but equivalent forms. And yet, the search for such a “one-way […]
Speaker: Michael Shulman - Dept. of Mathematics, University of San Diego Title: Homotopy type theory and the quest for extensionality Abstract: Over the past decades, dependent type theory has proven to be a powerful framework for verified software and formalized mathematics. However, its treatment of equality has always been somewhat uncomfortable. Recently, homotopy type theory has […]
Dan Freed (The University of Texas at Austin) Title: The Atiyah-Singer Index Theorem Abstract: The story of the index theorem ties together the Gang of Four—Atiyah, Bott, Hirzebruch, and Singer—and lies at the intersection of analysis, geometry, and topology. In the first part of the talk I will recount high points in the early developments. Then I […]