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<pre><font face="Helvetica, Arial, sans-serif">INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540
Mathematics Seminars
Week of September 15, 2014
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To view mathematics in titles and abstracts, please click on the talk's link.
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Tuesday, September 16
Topology of Algebraic Varieties
Topic: Hodge theory and derived categories of cubic fourfolds
Speaker: Richard Thomas, Imperial College London
Time/Room: 2:00pm - 3:00pm/S-101
Abstract Link: <a href="http://www.math.ias.edu/seminars/abstract?event=62615">http://www.math.ias.edu/seminars/abstract?event=62615</a>
Topology of Algebraic Varieties
Topic: Generic K3 categories and Hodge theory
Speaker: Daniel Huybrechts, University of Bonn
Time/Room: 3:30pm - 4:30pm/S-101
Abstract Link: <a href="http://www.math.ias.edu/seminars/abstract?event=62625">http://www.math.ias.edu/seminars/abstract?event=62625</a>
Thursday, September 18
Working Group on Algebraic Number Theory
Speaker: To Be Announced
Time/Room: 2:00pm - 4:00pm/Fine 401, Princeton University
Joint IAS/Princeton University Number Theory Seminar
Topic: Iwasawa main conjecture for supersingular elliptic curves
Speaker: Xin Wan, Columbia University
Time/Room: 4:30pm - 5:30pm/Fine 214, Princeton University
Abstract Link: <a href="http://www.math.ias.edu/seminars/abstract?event=62585">http://www.math.ias.edu/seminars/abstract?event=62585</a>
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<font face="Helvetica, Arial, sans-serif">
1 Hodge theory and derived categories of cubic fourfolds
<br>
Richard Thomas
<br>
<br>
</font>
<p><font face="Helvetica, Arial, sans-serif">Cubic fourfolds behave
in many ways like K3 surfaces. Certain cubics - conjecturally,
the ones that are rational - have specific K3s associated to
them geometrically. Hassett has studied cubics with K3s
associated to them at the level of Hodge theory, and Kuznetsov
has studied cubics with K3s associated to them at the level of
derived categories.
I will explain all this via some pretty explicit examples, and
then I will explain joint work with Addington showing that these
2 notions of having an associated K3 surface coincide
generically.
</font></p>
<font face="Helvetica, Arial, sans-serif"><a
href="http://www.math.ias.edu/seminars/abstract?event=62615">http://www.math.ias.edu/seminars/abstract?event=62615</a><br>
<br>
2 Generic K3 categories and Hodge theory
<br>
Daniel Huybrechts
<br>
<br>
</font>
<p><font face="Helvetica, Arial, sans-serif">In this talk I will
focus on two examples of K3 categories: bounded derived
categories of (twisted) coherent sheaves and K3 categories
associated with smooth cubic fourfolds. The group of
autoequivalences of the former has been intensively studied over
the years (work by Mukai, Orlov, Bridgeland and others), whereas
the investigation of the latter has only just began. As a
motivation, I shall recall Mukai's classification of finite
groups of automorphisms of K3 surfaces and its more recent
derived version which involves the Leech lattice. In the second
half I will discuss work in progress describing the group of
autoequivalences of the very general cubic K3 category in terms
of Hodge theory.
</font></p>
<font face="Helvetica, Arial, sans-serif"><a
href="http://www.math.ias.edu/seminars/abstract?event=62625">http://www.math.ias.edu/seminars/abstract?event=62625</a><br>
<br>
3 Iwasawa main conjecture for supersingular elliptic curves
<br>
Xin Wan
<br>
<br>
</font>
<p><font face="Helvetica, Arial, sans-serif">We will describe a new
strategy to prove the plus-minus main conjecture for elliptic
curves having good supersingular reduction at \(p\). It makes
use of an ongoing work of Kings-Loeffler-Zerbes on explicit
reciprocity laws for Beilinson-Flach elements to reduce to
another main conjecture of Greenberg type, which can in turn be
proved using Eisenstein congruences on the unitary group
\(U(3,1)\).
</font></p>
<font face="Helvetica, Arial, sans-serif"><a
href="http://www.math.ias.edu/seminars/abstract?event=62585">http://www.math.ias.edu/seminars/abstract?event=62585</a><br>
<br>
IAS Math Seminars Home Page:<br>
<a href="http://www.math.ias.edu/seminars">http://www.math.ias.edu/seminars</a></font>
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