Date/Time/Venue	Talks
Feb 10, 2023 (Fri) 9:30AM Zoom link	Speaker: Guofang Wei (University of California, Santa Barbara) Title: Manifolds/Singular Spaces with Ricci Curvature Lower Bound Abstract: It is of general interest to study the difference between Ricci and sectional curvature lower bound. A well known difference is their control on Betti numbers. Joint with J. Pan, we constructed manifolds/singular spaces with nonnegative Ricci curvature which give negative answers to two long open questions. One is about the properness of Busemann functions, and the other one regards the singular set of Ricci limit sets. Building on these, joint with X. Dai, S. Honda, J. Pan, we discover two surprising types of Weyl's laws which are fractal-like for some compact singular space with "Ricci lower bound" (Ricci limit spaces). These show dramatic new features for Ricci lower bound.
Feb 13, 2023 (Mon) 11:00AM LSB 222	Speaker: Lei Zhang (National University of Singapore) Title: Automorphic periods and Strongly tempered spherical varieties Abstract: The Rankin-Selberg method is a classical approach to constructing integral representations of L-functions. One may use it to obtain the meromorphic continuation and functional equations of many L-functions. In this talk, we will survey several important constructions of Rankin-Selberg integrals and explore the connection with the double flag varieties for symmetric pairs, which are classified by He, Nishiyama, Ochiai, and Oshima. Moreover, we will discuss some new cases of period integrals on the strongly tempered spherical varieties and give their conjectural identity of central values of L-functions and their local multiplicity formulas in terms of local symplectic root number.
Feb 17, 2023 (Fri) 1:00PM LSB 222	Speaker: Jongil Park (Seoul National University) Title: Symplectic fillings versus Milnor fibers of weighted homogeneous surface singularities Abstract: One of active research areas in symplectic 4-manifolds is to classify symplectic fillings of certain 3-manifolds equipped with a contact structure. Among them, people have long studied symplectic fillings of the link of a normal surface singularity. One the other hand, algebraic geometers also have studied Milnor fibers as a general fiber of smoothings for a normal surface singularity. In this talk, I'd like to review what we have obtained on minimal symplectic fillings of Seifert 3-manifolds and Milnor fibers of the corresponding weighted homogeneous surface singularities. The main parts of this work are joint with Hakho Choi.
Mar 3, 2023 (Fri) 4:30PM Zoom link	Speaker: Yao Yao (National University of Singapore) Title: Small scale formations in fluid equations with gravity Abstract: In this talk, we discuss some PDEs that describe fluid motion under the influence of gravity, including the incompressible porous media equation and incompressible Boussinesq equation in two dimensions. Using an interplay between various monotone and conserved quantities, we construct rigorous examples of small scale formations as time goes to infinity. These growth results work for a broad class of initial data, where we only require certain symmetry and sign conditions. As an application, we also construct solutions to the 3D axisymmetric Euler equation whose velocity has infinite-in-time growth. (Based on joint works with Alexander Kiselev and Jaemin Park).
Mar 21, 2023 (Tue) 2:00PM LSB 222	Speaker: Sam Payne (University of Texas at Austin) Title: Cohomology groups of moduli spaces of curves Abstract: The cohomology groups of moduli spaces of curves are important to several mathematical disciplines, from low-dimensional topology and geometric group theory to stable homotopy theory and quantum algebra. Algebraic geometry endows these groups with additional structures, such as Hodge structures and Galois representations, and the Langlands program makes striking predictions about which such structures can appear. I will survey recent results confirming several of these predictions and making progress toward calculating these groups and determining in which degrees they do and do not vanish.Based on joint work with Jonas Bergstrom and Carel Faber; with Sam Canning and Hannah Larson; with Melody Chan and Soren Galatius; and with Thomas Willwacher.
Mar 31, 2023 (Fri) 9:30AM Zoom link	Speaker: David Ben-Zvi (University of Texas, Austin) Title: Higher geometric quantization and L-functions Abstract: I'll describe a perspective on the theory of L-functions inspired by geometric quantization, developed in joint work with Yiannis Sakellaridis and Akshay Venkatesh. To a suitable class of hamiltonian actions of reductive groups one attaches two ``higher" quantization problems [in the sense of higher-dimensional QFT], one dubbed magnetic or automorphic and the other electric or spectral. Electric-magnetic / Langlands duality exchanges these quantization problems for dual reductive groups. I'll explain how, when considered in arithmetic contexts, the notion of automorphic quantization captures the theory of periods of automorphic forms, while spectral quantization captures the theory of L-functions of Galois representations.
Apr 14, 2023 (Fri) 9:30AM Zoom link	Speaker: Christina Sormani (Lehman College and CUNY Graduate Center) Title: Applying the Null Distance to define Spacetime Intrinsic Flat Convergence Abstract: In order to define a new notion of convergence for sequences of spacetimes, (Nj, gj), we plan to first convert the spacetimes into metric spaces endowed with time functions, (Xj, dj, τj). This can be done in a canonical way using the Andersson-Howard-Galloway Cosmological time function τj: Nj -> [0, τmax] on spacetimes where this time function is regular by taking the distance function dj to be the null distance defined by Sormani-Vega. Sakovich-Sormani proved that if τj is also proper then one can recover the causal structure from the information on (Xj, dj, τj). Applying this result combined with work of Hawking et al, they prove that if there is a time preserving isometry from (X1, d1, τ1) to (X2, d2, τ2), then there is a Lorentzian isometry from (N1, g1) to (N2, g2). This talk will present these results in detail and explain how this can next be applied to define a spacetime intrinsic flat convergence using this method. For more information about intrinsic flat convergence see here.
Apr 21, 2023 (Fri) 9:30AM Zoom link	Speaker: Juhi Jang (University of Southern California) Title: Dynamics of Newtonian star Abstract: A classical model to describe the dynamics of Newtonian stars is the gravitational Euler-Poisson system. The Euler-Poisson system admits a wide range of star solutions that are in equilibrium or expand for all time or collapse in a finite time or rotate. In this talk, I will discuss some recent progress on those star solutions with focus on expansion and collapse. If time permits, I will also discuss the non-radial stability of expanding Goldreich-Weber star solutions.