[csdm-rutgers] Mathematics Seminars -- Week of September 15, 2014

[Anthony Pulido]

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:	http://www.math.ias.edu/seminars/abstract?event=62615

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:	http://www.math.ias.edu/seminars/abstract?event=62625



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:	http://www.math.ias.edu/seminars/abstract?event=62585

1 Hodge theory and derived categories of cubic fourfolds
    Richard Thomas

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.

http://www.math.ias.edu/seminars/abstract?event=62615

2 Generic K3 categories and Hodge theory
    Daniel Huybrechts

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.

http://www.math.ias.edu/seminars/abstract?event=62625

3 Iwasawa main conjecture for supersingular elliptic curves
    Xin Wan

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 \(U(3,1)\).

http://www.math.ias.edu/seminars/abstract?event=62585

IAS Math Seminars Home Page:
http://www.math.ias.edu/seminars
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