For the schedule of talks please visit: http://scgp.stonybrook.edu/archives/30366
Speaker: Sergei Dubovsky
Title: "Hidden Symmetry of Vanishing Love"
Title: Higgs bundles and higher Teichmuller spaces
Speaker: Oscar Garcia-Prada [Institute of Mathematical Sciences (ICMAT, Madrid)]
Abstract: It is well-known that the Teichmuller space of a compact surface can be identified with a connected component of the moduli space of representations of the fundamental group of the surface in PSL(2,R). Higher Teichmueller spaces are generalizations of this, where PSL(2,R) is replaced by certain simple non-compact real Lie groups of higher rank. As for the usual Teichmuller space, these spaces consist entirely of discrete and faithful representations. Several cases have been identified over the years. First, the Hitchin components for split groups, then the maximal Toledo invariant components for Hermitian groups, and more recently certain components for SO(p,q). In this talk, I will describe a general construction of all possible higher Teichmuller spaces, and a parametrization of them using Higgs bundles given in joint work with Bradlow, Collier, Gothen and Oliveira.
Speaker: Yuji Odaka [Kyoto University]
Title: A Mathematician at the State Department
Speaker: Margaret Callahan [U.S. Department of State]
Abstract: Margaret Callahan is a conflict analyst in the Bureau of Conflict and Stabilization Operations (CSO) at the State Department. Margaret is CSO’s lead analyst for the Western Hemisphere. In this role, she uses data analysis and a range of quantitative methods to advance the bureau's mission to anticipate, prevent, and respond to global conflict. Margaret earned her Ph.D. in applied mathematics from Case Western Reserve University in 2016; her academic research focused on Bayesian statistical inverse problems.
Speaker: Chris Bishop
Title: Random thoughts on random sets
Abstract: I will discuss some open problems that I have thought about over the last 30 years. Some are well known (e.g., growth rate of DLA), but a new may be novel, such as the flow associated to a planar triangulation. There will be many pictures, results of some computer experiments, but very few theorems or proofs.
Title: Billiards and the arithmetic of non-arithmetic groups
Speaker: Curtis T. McMullen [Harvard University]
Title: Heat kernel and curvature bounds in Ricci flows with bounded scalar curvature, Advances in Mathematics, (2017), 319:396-450, R. Bamler-Q. Zhang
Speaker: Conghan Dong [Stony Brook University]
Title: Decomposition Theorem for Semisimple Local Systems
Speaker: Ruijie Yang [Stony Brook University]
Abstract: In complex algebraic geometry, the decomposition theorem asserts that semisimple geometric objects remain semisimple after taking direct images under proper algebraic maps. This was conjectured by Kashiwara and is proved by Mochizuki and Sabbah in a series of long papers via harmonic analysis and D-modules.
In this thesis defense, we would like to explain a simpler proof in the case of semisimple local systems, using a more geometric approach adapting de Cataldo-Migliorini. On the one hand, we complement Simpson’s theory of weights for local systems by proving a global invariant cycle theorem in the setting of local systems. On the other hand, we define a notion of polarization via Hermitian forms on pure twistor structures. This is partially based on joint work with Chuanhao Wei.