[math-ias] IAS Math Seminars -- Week of December 3, 3012
Dottie Phares
phares at ias.edu
Thu Nov 29 14:22:27 EST 2012
INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540
Mathematics Seminars
Week of December 3, 2012
Monday, December 3
Computer Science/Discrete Mathematics Seminar I
Topic: Information Complexity and Exact Communication
Bounds
Speaker: Mark Braverman, Princeton University
Time/Room: 11:15am - 12:15pm/S-101
Abstract: See below
Members Seminar
Topic: Quantum Mechanics -- a Primer for Mathematicians
Speaker: Juerg Frohlich, ETH Zurich; Member, School of
Mathematics
Time/Room: 2:00pm - 3:00pm/S-101
Abstract: See below
Univalent Foundations Tutorial
Time/Room: 4:00pm - 5:30pm/S-101
Tuesday, December 4
Computer Science/Discrete Mathematics Seminar II
Topic: Delegation for Bounded Space
Speaker: Ran Raz, Weizmann Institute; Member, School of
Mathematics
Time/Room: 10:30am - 12:30pm/S-101
Working Group on Univalent Foundations
Time/Room: 1:30pm - 2:45pm/S-101
Wednesday, December 5
Univalent Foundations Seminar
Topic: Type Systems
(continued)
Speaker: Vladimir Voevodsky, Professor, School of Mathematics,
IAS
Time/Room: 11:00am - 12:30pm/S-101
Working Group on Univalent Foundations
Time/Room: 1:30pm - 3:00pm/S-101
Workshop on Topology: Identifying Order in Complex Systems
** This Workshop will be held in conjunction with the symposium
"Through the Looking Glass" at the Princeton Center for Theoretical
Science
Topic: The Topology of DNA.
Speaker: Dorothy Buck, Imperial College London, UK
Time/Room: 2:00pm - 3:00pm/Princeton University, Jadwin Hall, Rm.
407
Topic: Discrete Morse Complexes and Skeletons from
Digital Images
Speaker: Vanessa Robins, Australian National University
Time/Room: 3:30pm - 4:30pm/Princeton University, Jadwin Hall, Rm.
407
Topic: Driving Forces in Comeocyte Expansion: A Geometric
Perspective
Speaker: Myfanwy Evans, Institute for Theoretical Physics,
University of Erlangen-Nuremberg
Time/Room: 5:00pm - 6:00pm/Princeton University, Jadwin Hall, Rm.
407
Mathematical Conversations
Topic: Checking Mathematical Proofs With a Computer
Speaker: Assia Mahboubi, INRIA (French National Institute for
Research in CS); Member, School of Mathematics
Time/Room: 6:00pm - 7:30pm/Dilworth Room
Abstract: See below
Thursday, December 6
Univalent Foundations Seminar
Topic: The Simplicial Model of Univalence
(continued)
Speaker: Peter Lumsdaine, Dalhousie University; Member, School
of Mathematics
Time/Room: 11:00am - 12:30pm/S-101
Working Group on Algebraic Number Theory
Time/Room: 2:00pm - 4:00pm/Fine Hall -- 801
Joint IAS/PU Number Theory Seminar
Topic: Monodromy and Arithmetic Groups
Speaker: T. N. Venkataramana, Tata Institute of Fundamental
Research
Time/Room: 4:30pm - 5:30pm/Fine Hall 214
Abstract: See below
Friday, December 7
Working Group on Univalent Foundations
Time/Room: 11:00am - 12:30pm/S-101
Analysis Seminar
Topic: Nonlinear Long-Range Resonant Scattering and Kink
Dynamics
Speaker: Avy Soffer, Rutgers, The State University of New
Jersey
Time/Room: 3:15pm - 4:15pm/S-101
Abstract: See below
Joint IAS-PU Symplectic Geometry Seminar
Topic: Open-Closed Gromov-Witten Invariants of Toric
Calabi-Yau 3-Orbifolds
Speaker: Chiu-Chu Melissa Liu, Columbia University
Time/Room: 4:30pm - 5:30pm/S-101
Abstract: See below
1 Information Complexity and Exact Communication Bounds
Mark Braverman
In this talk we will discuss information complexity -- a measure of the
amount of information Alice
and Bob need to exchange to solve a problem over distributed inputs. We will
present an
information-theoretically optimal protocol for computing the AND of two bits
distributed between
Alice and Bob. We prove that the information complexity of AND is ~1.4923
bits. We use the optimal
protocol and its properties to obtain tight bounds for the Disjointness
problem, showing that the
randomized communication complexity of Disjointness on n bits is ~0.4827n ±
o(n).
Based on joint work with Ankit Gard, Denis Pankratov, and Omri Weinstein
2 Quantum Mechanics -- a Primer for Mathematicians
Juerg Frohlich
A general algebraic formalism for the mathematical modeling of physical
systems is sketched. This
formalism is sufficiently general to encompass classical and
quantum-mechanical models. It is then
explained in which way quantum theory differs in an essential way from
classical theory and what it
is that quantum theory tells us about Nature when suitable experiments are
made. Some of the
seemingly confusing aspects of quantum theory are highlighted, and it is
explained why they actually
should not confuse us. A variety of concrete problems of potential interest
to mathematicians will
be mentioned.
3 Checking Mathematical Proofs With a Computer
Assia Mahboubi
Black (or white) board is probably one of the most precious companions to
many mathematicians.
However, computers now also play an increasing role in the everyday activity
of a researcher in
mathematics: for typesetting articles, for testing conjectures, and
sometimes even for validating
parts of proofs by large computations.
A maybe less known family of software, called proof assistants, also aim at
``doing mathematics with
a computer". These systems allow their users to check with the highest
degree of certainty the
validity of the proofs they have carefully described to the machine.
A first landmark was obtained in 2005 with the complete verification by such
a proof assistant of
the controversial proof of the Four Colour Theorem, which combines
combinatorial reasoning with
large scale computations beyond the reach of pen and paper calculations.
Last September a proof of the Odd Order
Theorem (Feit-Thompson, 1963), which is a milestone for the Enormous Theorem
of the classification
of finite simple groups, has also been verified by the Coq proof assistant.
This time, the computer
is used to check a proof which does not rely on heavy computations but on a
sophisticated
combination of mathematical theories resulting in the longest published
proof at its time.
We will see how this last achievement illustrates the quite wide variety of
research areas and
methodologies that should combine in order to ensure the success of such a
project. Black (or white)
board will eventually never be surpassed to convey and give rise to the
intuitions of the mind who discovers
new mathematics, but having proofs checked by a machine rather by a human
reviewer may open some new
perspectives we will hopefully discuss.
4 Monodromy and Arithmetic Groups
T. N. Venkataramana
Monodromy groups arise naturally in algebraic geometry and in differential
equations, and often
preserve an integral lattice. It is of interest to know whether the
monodromy groups are arithmetic
or thin.
In this talk we review the Deligne-Mostow theory and show that for cyclic
coverings of degree $d$ of
the projective line, with a prescribed number $m$ of branch points and
prescribed ramification
indices, the monodromy is an arithmetic group provided $m\geq 2d-2$. This is
closely related to the
arithmeticity of the image of the Burau representation at $d$-th roots of
unity.
We also show that the monodromy asociated to certain hypergeometric
differential equations of type
$_n F_n-1$ is arithmetic in a number of cases, providing a counterpart to
results of
Fuchs-Meiri-Sarnak and of Brav-Thomas.
5 Nonlinear Long-Range Resonant Scattering and Kink Dynamics
Avy Soffer
We study the nonlinear Klein-Gordon equation, in one dimension, with a
qudratic term and variable
coefficient qubic term. This equation arises from the asymptotic stability
theory of the kink
solution.Our main result is the global existence and decay estimates for
this equation. We
discovered a striking new phenomena in this problem: a resonant interaction
between the spacial
frequencies of the nonlinear coefficient and the temporal oscillations of
the solution.
The proof requires the development of new normal-form transformations. This
is a joint work with H.
Lindblad, I. Rodnianski and J. Sterbenz.
6 Open-Closed Gromov-Witten Invariants of Toric Calabi-Yau
3-Orbifolds
Chiu-Chu Melissa Liu
We study open-closed orbifold Gromov-Witten invariants of toric Calabi-Yau
3-orbifolds with respect
to Lagrangian branes of Aganagic-Vafa type. We prove an open mirror theorem
which expresses
generating functions of orbifold disk invariants in terms of Abel-Jacobi
maps of the mirror curves.
This is a joint work with Bohan Fang and Hsian-Hua Tseng.
IAS Math Seminars Home Page:
http://www.math.ias.edu/seminars
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