Talk_id | Date | Speaker | Title |
26960
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Wednesday 1/27 4:00 PM
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Vaidehee Thatte, SUNY Binghamton
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Arbitrary Valuation Rings and Wild Ramification
- Vaidehee Thatte, SUNY Binghamton
- Arbitrary Valuation Rings and Wild Ramification
- 01/27/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Preston Wake (wakepres@msu.edu)
We aim to develop ramification theory for arbitrary valuation fields, extending the classical theory of complete discrete valuation fields with perfect residue fields. By studying wild ramification, we hope to understand the mysterious phenomenon of the $\textit{defect}$ (or ramification deficiency) unique to the positive residue characteristic case and is one of the main obstacles in obtaining resolution of singularities.
Extensions of degree $p$ in residue characteristic $p>0$ are building blocks of the general case. We present a generalization of ramification invariants for such extensions. These results enable us to construct an upper ramification filtration of the absolute Galois group of Henselian valuation fields (joint with K.Kato).
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26988
|
Wednesday 2/3 4:00 PM
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Laure Flapan, MSU
|
Fano manifolds associated to hyperkähler manifolds
- Laure Flapan, MSU
- Fano manifolds associated to hyperkähler manifolds
- 02/03/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Laure Flapan (flapanla@msu.edu)
Many of the known examples of hyperkähler manifolds arise from geometric constructions that begin with a Fano manifold whose cohomology looks like that of a K3 surface. In this talk, I will focus on a program whose goal is to reverse this process, namely to begin with a hyperkähler manifold and from it produce geometrically a Fano manifold. This is joint work in progress with K. O’Grady, E. Macrì, and G. Saccà.
Passcode: MSUALG
|
26954
|
Wednesday 2/10 4:00 PM
|
Tudor Padurariu, IAS
|
Noncommutative resolutions and intersection cohomology for quotient singularities
- Tudor Padurariu, IAS
- Noncommutative resolutions and intersection cohomology for quotient singularities
- 02/10/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Laure Flapan (flapanla@msu.edu)
It is an important problem to define a K-theoretic version of intersection cohomology, with expected applications in representation theory. One step further is to look for a categorification of intersection cohomology. For good moduli spaces $X$ of Artin stack $Y$ (as defined by Alper), we construct some noncommutative resolutions $D(X)$ inside the category $D^b(Y)$. Further, we construct subcategories $I(X)$ of $D(X)$ whose periodic cyclic homology is given by the intersection cohomology of $X$. In particular, the K-theory of $I(X)$ is a natural definition of intersection K-theory for the variety $X$.
Passcode: MSUALG
|
26957
|
Wednesday 2/17 4:00 PM
|
François Greer, IAS
|
A tale of two Severi curves
- François Greer, IAS
- A tale of two Severi curves
- 02/17/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Laure Flapan (flapanla@msu.edu)
Let $(S,L)$ be a general polarized K3 surface with $c_1(L)^2=2g-2$. A general member of the linear system $|L|\simeq \mathbb P^g$ is a smooth curve of genus $g$. For $0\leq h\leq g$, define the Severi variety $V_h(S,L)\subset |L|$ to be the locus of curves with geometric genus $\leq h$. As expected, $V_h(S,L)$ has dimension $h$. We consider the case $h=1$, where the Severi variety is a (singular) curve. Our first result is that the geometric genus of $V_1(S,L)$ goes to infinity with $g$; we give a lower bound $\sim e^{c\sqrt{g}}$. Next we consider the analogous question for Severi curves of a rational elliptic surface, and give a polynomial upper bound instead. Modular forms play a central role in both arguments.
Passcode: MSUALG
|
26958
|
Wednesday 2/24 4:00 PM
|
Ignacio Barros, Université Paris-Saclay
|
Pencils on surfaces with normal crossings and the Kodaira dimension of $M_{g,n}$
- Ignacio Barros, Université Paris-Saclay
- Pencils on surfaces with normal crossings and the Kodaira dimension of $M_{g,n}$
- 02/24/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Laure Flapan (flapanla@msu.edu)
The first half of the talk will be a colloquium style talk, where I will recall the history of the problem of determining the Kodaira dimension of the moduli space of curves. In the second half I will report on joint work with D. Agostini, where we study smoothing of pencils of curves on surfaces with normal crossings. As a consequence we obtain new instances of $(g,n)$ where $M_{g,n}$ is of negative Kodaira dimension and provide bounds for the Kodaira dimension of $M_{16}$ and $M_{12,8}$.
Passcode: MSUALG
|
26956
|
Wednesday 3/3 4:00 PM
|
Rankeya Datta, University of Illinois at Chicago
|
Openness of splinter loci in prime characteristic.
- Rankeya Datta, University of Illinois at Chicago
- Openness of splinter loci in prime characteristic.
- 03/03/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Joe Waldron (waldro51@msu.edu)
A splinter is a notion of singularity that has seen numerous applications of late, especially in connection with the direct summand theorem, the mixed characteristic minimal model program, Cohen-Macaulayness of absolute integral closures and vanishing theorems. However, many basic questions about splinters remain elusive. One such problem is whether the splinter condition spreads from a point to an open neighborhood of a noetherian scheme. In this talk, we will address this question in prime characteristic and show that a locally noetherian scheme whose associated
absolute Frobenius is finite map has an open splinter locus. In particular,
all varieties over perfect fields of positive characteristic have open splinter loci. If time permits, we will show how our methods also give openness of splinter loci for a large class of schemes that do not necessarily have finite Frobenius. This talk is based on joint work in progress with Kevin Tucker.
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26987
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Wednesday 3/10 4:00 PM
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Joe Waldron, MSU
|
Minimal model program for threefolds of mixed characteristic
- Joe Waldron, MSU
- Minimal model program for threefolds of mixed characteristic
- 03/10/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
- Laure Flapan (flapanla@msu.edu)
A major obstacle to extending the minimal model program away from characteristic zero is the lack of cohomology vanishing theorems such as Kodaira vanishing. In this talk we describe the minimal model program and then discuss a new way to overcome this difficulty in the arithmetic situation, which has enabled the development of the minimal model program for arithmetic threefolds of residue characteristic greater than 5. This is joint work with Bhatt, Ma, Patakfalvi, Schwede, Tucker and Witaszek.
|
26955
|
Wednesday 3/17 4:00 PM
|
Daniel Bragg, University of California, Berkeley
|
TBA
- Daniel Bragg, University of California, Berkeley
- TBA
- 03/17/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
- Rajesh S Kulkarni (kulkar23@msu.edu)
No abstract available.
|
26977
|
Wednesday 3/24 4:00 PM
|
Stefan Patrikis, Ohio State University
|
TBA
- Stefan Patrikis, Ohio State University
- TBA
- 03/24/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
- Igor Rapinchuk (rapinchu@msu.edu)
No abstract available.
|
26997
|
Wednesday 3/31 4:00 PM
|
Oscar Rivero, University of Warwick
|
TBA
- Oscar Rivero, University of Warwick
- TBA
- 03/31/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
- Preston Wake (wakepres@msu.edu)
No abstract available.
|
26952
|
Wednesday 4/7 4:00 PM
|
Sarah Frei, Rice University
|
TBA
- Sarah Frei, Rice University
- TBA
- 04/07/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
- Rajesh S Kulkarni (kulkar23@msu.edu)
No abstract available.
|
26959
|
Wednesday 4/14 4:00 PM
|
Yihang Zhu, University of Maryland
|
TBA
- Yihang Zhu, University of Maryland
- TBA
- 04/14/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
- Igor Rapinchuk (rapinchu@msu.edu)
No abstract available.
|
26996
|
Wednesday 4/21 4:00 PM
|
Jonathan Wang, MIT
|
TBA
- Jonathan Wang, MIT
- TBA
- 04/21/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
- Preston Wake (wakepres@msu.edu)
No abstract available.
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