Title: The Quillen-Lichtenbaum dimension of an algebraic variety and the integral Hodge conjecture.Abstract: I will explain a numerical invariant of complex varieties born out of the difference between algebraic and topological K-theory. In some cases, it is a birational invariant which is weaker than some known ones coming from unramified cohomology. However, it is also a derived […]
Title: Compatibility of canonical ell-adic local systems on Shimura varieties Abstract: In his 1979 Corvallis paper, Deligne uses a modular interpretation to construct canonical models of Shimura varieties of Hodge type, and suggested a dream that all Shimura varieties with rational weight should be moduli spaces of motives over number fields. Outside of the abelian […]
Title: The stability of irrotational shocks and the Landau law of decay. Abstract: We consider the long-time behavior of irrotational solutions of the three-dimensional compressible Euler equations with shocks, hypersurfaces of discontinuity across which the Rankine-Hugoniot conditions for irrotational flow hold. Our analysis is motivated by Landau's analysis of spherically-symmetric shock waves, who predicted that at large times, […]
Title: Decategorifying the singular support of coherent sheaves Abstract: The microlocal homology is a family of chain theories that interpolates between the Borel–Moore homology and singular cohomology of a complex variety in the case when that variety is singular and Poincaré duality fails. Such a device allows one to speak of the singular support […]
Title: On the isoperimetric profile of the hypercube Abstract: The isoperimetric problem in the hypercube is a strikingly simple topic which is not yet completely understood. We will review the known facts on the problem, focusing on how the gaussian isoperimetric inequality provides a lower bound for the isoperimetric profile of the hypercube.We will exploit this […]
Title: Analytic rings
Title: Fibered Yoneda Lemma in Lean 4 Abstract: In this talk, I would like to give you a sense of what it’s like to do category theory in a computer. I use an interactive theorem prover called Lean4, a complex piece of software based on dependent type theory. In the first part, I will give a quick […]
Title: Abstract:
Dr. Riehl will be giving an interactive talk where we will play the natural numbers game and learn about formalizing mathematics in a computer-proof assistant! We ask that everyone who attends bring a laptop so that they can more easily participate.
Title: The Geometry of Theta Correspondence for Principal Series over Finite Fields Abstract: In this talk, we explore the finite field theta correspondence between principal series representations. We begin by categorifying the relevant Hecke algebra bimodules associated with this correspondence. Utilizing characteristic cycle maps, we provide a detailed description of the theta correspondence for principal […]
Title: From Instability to Singularity Formation in Incompressible FluidsAbstract: In this talk, I will first review the singularity formation problem in incompressible fluid dynamics, describing how particle transport poses the main challenge in constructing blow-up solutions for the 3d incompressible Euler equations. I will then outline a new mechanism that allows us to overcome the effects of […]
Title: ell-adic topological Jacquet-Langlands duality Abstract: I will describe the construction of an "ell-adic topological Jacquet-Langlands (TJL) dual" of each finite CW-complex. One effect of the TJL dual is that the representations of the Morava stabilizer group, which arise in the height n Morava E-theory of a finite spectrum X, get turned into continuous […]