Formal GAGA for Brauer classes
Abstract: The relationship between analytic and algebraic geometry (GAGA) is a rich area of study. For example, Grothendieck's existence theorem states that if X is proper over a complete local Noetherian ring A, then a coherent sheaf on the formal scheme X^, a priori only definable using formal power series, is actually algebraic. Such GAGA-type results are now standard tools for studying varieties and their families. One sample consequence: a compatible system of line bundles L_n on the thickenings X_n of the special fiber of X/Auniquely algebraizes to a line bundle L on X. In this talk, we answer a question Grothendieck posed in the 1960s about Brauer classes: can a Brauer class be determined from a compatible system of classes on the X_n? This is joint work with Andrew Kresch.
Event Type: Seminar. Research Area: Algebra and Number Theory. Location: MSC W303. Speaker Name: Siddharth Mathur. Speaker Institution: University of Georgia.
Tuesday, September 16, 2025, 4:00 PM – 5:00 PM.
Well-Posedness, Stability, and Bifurcation for Keller-Segel Models on Compact Graphs
Abstract: In this talk, we will discuss the Keller-Segel model describing various chemotaxis processes. The system of PDEs in question is a pair of reaction-advection-diffusion equations of parabolic and elliptic type. The first part of the talk will center around well-posedness of this system on arbitrary compact metric graphs. In the second part of the talk, we will focus on asymptotic stability, instability, and bifurcation of steady state solutions of parabolic-parabolic and parabolic-elliptic chemotaxis models. This is joint work with Hewan Shemtaga (UIUC) and Wenxian Shen (Auburn).
Event Type: Seminar. Research Area: Analysis and Differential Geometry. Location: MSC W301. Speaker Name: Selim Sukhtaiev. Speaker Institution: Auburn University.
Friday, September 19, 2025, 11:00 AM – 12:00 PM.
From Teichmüller to Shoen–Yau: Extremal mappings between Riemann surfaces
Abstract: There are two now classical descriptions of the moduli space of a Riemann surface via the theory of extremal mappings. The first from Teichmu ̈ller in the 1940s (rigorously es- tablished by Ahlfors in 1953) and through the existence of extremal quasiconformal mappings. The second is through Schoen-Yau’s existence theory for unique harmonic diffeomorphisms in the 1970s, and developed into a theory of moduli by many, including Wolf, Tromba and Wolpert many years later. The important ingredient in both is the existence of a holomorphic quadratic differential, from the Beltrami coefficient of an extremal quasiconformal mapping (Teichmu ̈ller) or from the Hopf equation (Harmonic). These quadratic differentials define the cotangent space to the moduli space. Here we show that in fact both of these approaches are manifestations of the same theory (that of existence of diffeomorphic extremal mappings of finite distortion) in limiting regimes. We identify parameterised families of moduli spaces (Beltrami coe…
Event Type: Seminar. Research Area: Analysis and Differential Geometry. Location: MSC E408. Speaker Name: Professor Gaven Martin. Speaker Institution: Massey University (New Zealand).
Wednesday, October 22, 2025, 4:00 PM – 5:00 PM.