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<div class="moz-text-flowed" style="font-family: -moz-fixed;
font-size: 14px;" lang="x-unicode">INSTITUTE FOR ADVANCED STUDY
<br>
School of Mathematics
<br>
Princeton, NJ 08540
<br>
<br>
Mathematics Seminars
<br>
Week of October 6, 2014<br>
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To view mathematics in titles and abstracts, please click on the
talk's link.
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****UPDATE: Abstract added.****
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<br>
Joint IAS/Princeton University Number Theory Seminar
<br>
Topic: Euler systems from special cycles on unitary
Shimura varieties and arithmetic applications
<br>
Speaker: Dimitar Jetchev, École Polytechnique Fédérale de
Lausanne
<br>
Time/Room: 4:30pm - 5:30pm/Fine 214, Princeton University
<br>
Abstract Link: <a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=60805">http://www.math.ias.edu/seminars/abstract?event=60805</a>
<br>
<br>
Euler systems from special cycles on unitary Shimura varieties and
arithmetic applications
<br>
Dimitar Jetchev
<br>
<br>
We construct a new Euler system from a collection of special
1-cycles on certain Shimura 3-folds associated to \(U(2,1) \times
U(1,1)\) and appearing in the context of the Gan--Gross--Prasad
conjectures. We study and compare the action of the Hecke algebra
and the Galois group on these cycles via distribution relations
and congruence relations obtain adelically using Bruhat--Tits
theory for the corresponding buildings. If time permits, we
explain some potential arithmetic applications in the context of
Selmer groups and the Bloch--Kato conjectures for Galois
representations associated to automorphic forms on unitary groups.
<br>
<br>
<br>
<br>
Monday, October 6
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Computer Science/Discrete Mathematics Seminar I
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Topic: The communication complexity of distributed
subgraph detection
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Speaker: Rotem Oshman, Tel Aviv University
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Time/Room: 11:15am - 12:15pm/S-101
<br>
Abstract Link: <a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=52304">http://www.math.ias.edu/seminars/abstract?event=52304</a>
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<br>
Members' Seminar
<br>
Topic: Hodge theory, coniveau and algebraic cycles
<br>
Speaker: Claire Voisin, Centre national de la recherche
scientifique; Distinguished Visiting Professor, School of
Mathematics
<br>
Time/Room: 2:00pm - 3:00pm/S-101
<br>
Abstract Link: <a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=47531">http://www.math.ias.edu/seminars/abstract?event=47531</a>
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Tuesday, October 7
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Computer Science/Discrete Mathematics Seminar II
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Topic: Monotone submodular maximization over a matroid
<br>
Speaker: Yuval Filmus, Member, School of Mathematics
<br>
Time/Room: 10:30am - 12:30pm/S-101
<br>
Abstract Link: <a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=63175">http://www.math.ias.edu/seminars/abstract?event=63175</a>
<br>
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Topology of Algebraic Varieties
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Topic: On Euler-Poincaré characteristics
<br>
Speaker: Mark Andrea de Cataldo, Stony Brook University;
Member, School of Mathematics
<br>
Time/Room: 11:00am - 12:30pm/Physics Library, Bloomberg Hall
201
<br>
Abstract Link: <a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=64384">http://www.math.ias.edu/seminars/abstract?event=64384</a>
<br>
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Topology of Algebraic Varieties
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Topic: Chow rings and modified diagonals
<br>
Speaker: Kieran O'Grady, Sapienza - Università di Roma;
Member, School of Mathematics
<br>
Time/Room: 2:00pm - 3:00pm/S-101
<br>
Abstract Link: <a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=63484">http://www.math.ias.edu/seminars/abstract?event=63484</a>
<br>
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Topology of Algebraic Varieties
<br>
Topic: Two counterexamples arising from infinite sequences
of flops
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Speaker: John Lesieutre, Member, School of Mathematics
<br>
Time/Room: 3:30pm - 4:30pm/S-101
<br>
Abstract Link: <a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=63494">http://www.math.ias.edu/seminars/abstract?event=63494</a>
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Wednesday, October 8
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Topology of Algebraic Varieties
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Topic: The construction problem for Hodge numbers
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Speaker: Stefan Schreieder, University of Bonn
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Time/Room: 11:15am - 12:15pm/S-101
<br>
Abstract Link: <a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=63734">http://www.math.ias.edu/seminars/abstract?event=63734</a>
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Mathematical Conversations
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Topic: Randomness in the Mobius function and dynamics
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Speaker: Peter Sarnak, Professor, School of Mathematics
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Time/Room: 6:00pm - 7:00pm/Dilworth Room
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Thursday, October 9
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Working Group on Algebraic Number Theory
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Speaker: To Be Announced
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Time/Room: 2:00pm - 4:00pm/Fine 401, Princeton University
<br>
<br>
Joint IAS/Princeton University Number Theory Seminar
<br>
Topic: Euler systems from special cycles on unitary
Shimura varieties and arithmetic applications
<br>
Speaker: Dimitar Jetchev, École Polytechnique Fédérale de
Lausanne
<br>
Time/Room: 4:30pm - 5:30pm/Fine 214, Princeton University
<br>
Abstract Link: <a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=60805">http://www.math.ias.edu/seminars/abstract?event=60805</a>
<br>
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Friday, October 10
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Princeton/IAS Symplectic Geometry Seminar
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Topic: Superconformal simple type and Witten's conjecture
on the relation between Donaldson and Seiberg-Witten invariants
<br>
Speaker: Paul Feehan, Rutgers University
<br>
Time/Room: 1:30pm - 2:30pm/Fine 322, Princeton University
<br>
Abstract Link: <a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=59665">http://www.math.ias.edu/seminars/abstract?event=59665</a>
<br>
<br>
1 The communication complexity of distributed subgraph detection
<br>
Rotem Oshman
<br>
<br>
In distributed systems, communication between the participants in
the computation is usually the most expensive part of the
computation. Theoretical models of distributed systems usually
reflect this by neglecting the cost of local computation, and
charging only for messages sent between the participants; in
particular, we usually assume that the computation proceeds in
rounds, and in each round each participant can send only a limited
number of bits. We are interested in characterizing the number of
rounds required to perform various tasks. In this talk we discuss
the complexity of distributed subgraph detection: there are \(n\)
servers, each representing a node in an undirected graph, and each
server receives as input its adjacent edges in the graph. The goal
of the computation is to determine whether the global input graph
contains some fixed subgraph. In the talk I will describe upper
and lower bounds for several classes of subgraphs, through a
connection to Turan numbers. The general case remains open. We
also point out a connection between this problem and
number-on-forehead communication complexity, through which we are
able to obtain a tight lower bound on deterministic triangle
detection.
<br>
<br>
<a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=52304">http://www.math.ias.edu/seminars/abstract?event=52304</a>
<br>
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2 Hodge theory, coniveau and algebraic cycles
<br>
Claire Voisin
<br>
<br>
My talk will be a broad introduction to what is the (mostly
conjectural) higher dimensional generalization of Abel's theorem
on divisors on Riemann surfaces, namely, the relationship between
the structure of the group of algebraic cycles on a complex
projective variety and the complexity of its so-called Hodge
structures.
<br>
<br>
<a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=47531">http://www.math.ias.edu/seminars/abstract?event=47531</a>
<br>
<br>
3 Monotone submodular maximization over a matroid
<br>
Yuval Filmus
<br>
<br>
Monotone submodular maximization over a matroid (MSMM) is a
fundamental optimization problem generalizing Maximum Coverage and
MAX-SAT. Maximum Coverage is NP-hard to approximate better than
\(1-1/e\), an approximation ratio obtained by the greedy
algorithm. The performance of the greedy algorithm deteriorates to
\(1/2\) on the more general problem of MAX-SAT. Recently, Vondrak
et al. designed a sophisticated algorithm attaining the optimal
approximation ratio \(1-1/e\) for MSMM. Their algorithm finds a
fractional solution for a continuous relaxation of MSMM, and then
rounds it to a solution of the original problem. We present a
completely different algorithm which employs the paradigm of
non-oblivious local search and is completely combinatorial.
<br>
<br>
<a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=63175">http://www.math.ias.edu/seminars/abstract?event=63175</a>
<br>
<br>
4 On Euler-Poincaré characteristics
<br>
Mark Andrea de Cataldo
<br>
<br>
Report on R. Virk's arXiv:1406.4855v3. This is a fun, short and
simple note with variations on the well-known theme by G. Laumon
that the Euler characteristics with and without compact supports
coincide.
<br>
<br>
<a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=64384">http://www.math.ias.edu/seminars/abstract?event=64384</a>
<br>
<br>
5 Chow rings and modified diagonals
<br>
Kieran O'Grady
<br>
<br>
Beauville and Voisin proved that decomposable cycles
(intersections of divisors) on a projective K3 surface span a
1-dimensional subspace of the (infinite-dimensional) group of
0-cycles modulo rational equivalence. I will address the following
question: what is the rank of the group of decomposable 0-cycles
of a smooth projective variety? Beauville and Voisin also proved a
refinement of the result mentioned above, namely a decomposition
(modulo rational equivalence) of the small diagonal in the cube of
a K3. Motivated by this result we will discuss modified diagonals
and their relation with conjectures of Beauville and Voisin on the
Chow ring of hyperkaehler varieties.
<br>
<br>
<a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=63484">http://www.math.ias.edu/seminars/abstract?event=63484</a>
<br>
<br>
6 Two counterexamples arising from infinite sequences of flops
<br>
John Lesieutre
<br>
<br>
I will explain how infinite sequences of flops give rise to some
interesting phenomena: first, an infinite set of smooth projective
varieties that have equivalent derived categories but are not
isomorphic; second, a pseudoeffective divisor for which the
asymptotic multiplicity along a certain subvariety is infinite, in
the relative setting.
<br>
<br>
<a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=63494">http://www.math.ias.edu/seminars/abstract?event=63494</a>
<br>
<br>
7 The construction problem for Hodge numbers
<br>
Stefan Schreieder
<br>
<br>
What are the possible Hodge numbers of a smooth complex projective
variety? We construct enough varieties to show that many of the
Hodge numbers can take all possible values satisfying the
constraints given by Hodge theory. For example, there are
varieties such that a Hodge number \(h^{p,0}\) is big and the
intermediate Hodge numbers \(h^{i,p-i}\) are small.
<br>
<br>
<a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=63734">http://www.math.ias.edu/seminars/abstract?event=63734</a>
<br>
<br>
8 Euler systems from special cycles on unitary Shimura varieties
and arithmetic applications
<br>
Dimitar Jetchev
<br>
<br>
We construct a new Euler system from a collection of special
1-cycles on certain Shimura 3-folds associated to \(U(2,1) \times
U(1,1)\) and appearing in the context of the Gan--Gross--Prasad
conjectures. We study and compare the action of the Hecke algebra
and the Galois group on these cycles via distribution relations
and congruence relations obtain adelically using Bruhat--Tits
theory for the corresponding buildings. If time permits, we
explain some potential arithmetic applications in the context of
Selmer groups and the Bloch--Kato conjectures for Galois
representations associated to automorphic forms on unitary groups.
<br>
<br>
<a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=60805">http://www.math.ias.edu/seminars/abstract?event=60805</a>
<br>
<br>
9 Superconformal simple type and Witten's conjecture on the
relation between Donaldson and Seiberg-Witten invariants
<br>
Paul Feehan
<br>
<br>
We shall discuss two new results concerning gauge-theoretic
invariants of "standard" four-manifolds, namely closed, connected,
four-dimensional, orientable, smooth manifolds with \(b<sup
class="moz-txt-sup"><span
style="display:inline-block;width:0;height:0;overflow:hidden">^</span>1</sup>=0\)
and \(b+ \geq 3\) and odd. We first describe how the SO(3)
monopole link-pairing formula from Feehan and Leness (2002)
implies that all standard four-manifolds with Seiberg-Witten
simple type satisfy the superconformal simple type condition
defined by Marino, Moore, and Peradze (1999). This result implies
a lower bound, conjectured by Fintushel and Stern (2001), on the
number of Seiberg-Witten basic classes in terms of topological
data. In addition, we explain how the SO(3)-monopole cobordism
formula of Feehan and Leness (2002) and the superconformal simple
type property are used to prove Witten's Conjecture (1994)
relating the Donaldson and Seiberg-Witten invariants. References:
<a class="moz-txt-link-freetext"
href="http://arxiv.org/abs/1408.5307">http://arxiv.org/abs/1408.5307</a>,
<a class="moz-txt-link-freetext"
href="http://arxiv.org/abs/1408.5085">http://arxiv.org/abs/1408.5085</a>,
and <a class="moz-txt-link-freetext"
href="http://arxiv.org/abs/math/0203047">http://arxiv.org/abs/math/0203047</a>
<br>
<br>
<a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars/abstract?event=59665">http://www.math.ias.edu/seminars/abstract?event=59665</a>
<br>
<br>
IAS Math Seminars Home Page:
<br>
<a class="moz-txt-link-freetext"
href="http://www.math.ias.edu/seminars">http://www.math.ias.edu/seminars</a>
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