April 21 12PM-1PM APM 6402 Linquan Ma (University of Utah)
Title: Homological conjectures and big Cohen-Macaulay algebras Abstract: I will talk about joint work with Raymond Heitmann that gives a construction of big Cohen-Macaulay algebra in mixed characteristics following the recent breakthroughs on the direct summand conjecture by Andr\'{e} and Bhatt. In fact, we prove a weakly functorial version for certain surjective ring homomorphism that leads to the solution of the vanishing conjecture for maps of Tor in mixed characteristic. Our work also gives a simplified proof of the direct summand conjecture, and that direct summand of regular rings are Cohen-Macaulay. |
May 12 Yefeng Shen (Stanford)
Title: LG/CY correspondence in dimension one I will talk about Gromov-Witten theory of Calabi-Yau one-folds and Fan-Jarvis-Ruan-Witten theory of counterpart Landau-Ginzburg models. The GW invariants and FJRW invariants are enumerative counting of stable maps and sections of certain orbifold line bundles. We prove these invariants are coefficients of expansions of appropriate quasi-modular forms at different points, thus can be related by Cayley transformations. Abstract: |
May 19-21 Geometry of Moduli Spaces (Special Conference)
Conference home page |
May 26 Daniel Smith (UCSD)
Title: Some techniques for formal schemes Abstract: I will discuss recent approaches to working with formal schemes, including details from both proofs in my thesis and in the work of others. |
June 2 Morgan Brown (Miami)
Title: Points on del Pezzo surfaces in mixed characteristic Abstract: The Graber-Harris-Starr theorem says that any family of smooth rationally connected varieties over a complex curve has a section. A natural analogue of this statement in mixed characteristic would be that every rationally connected variety over the maximal unramified extension of a p-adic field has a rational point. I will discuss a geometric approach to this problem, as well as a proof of this statement for del Pezzo surfaces (for p>3). This is joint work with David Zureick-Brown. |
June 9 Michael McQuillan (Rome Tor Vergata)
Title: Semi-stable reduction of foliations Abstract: The talk will indicate the key features in the proof of the minimal model theorem for foliations by curves, which despite their possibly chaotic nature more closely parallels semi-stable reduction of curves (in arbitrary dimension) rather than the MMP for varieties. Indeed since vanishing theorems are false, it is ironically Mori Theory as Mori intended since everything must be done via the study of invariant rational curves. Highlights include simple local criteria for canonical foliation singularities, a simple classification of (foliated) Fano objects, and an explicit (foliated) flip theorem by way of the study of formal neighbourhoods of extremal rays. |
Organizers: Elham Izadi, James McKernan and Dragos Oprea
This seminar is supported in part by grants from the NSF. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Past quarters: Fall 2013 , Winter 2014 , Spring 2014 .
The design of this webpage is copied shamelessly from the MIT Number Theory seminar site. Contact Cal Spicer at cwspicer@ucsd.edu about problems with the website or posters.