[math-ias] IAS Math Seminars -- Week of November 19, 2012

[Dottie Phares]

INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540
 
Mathematics Seminars
Week of November 19, 2012
 
 
 
 
Monday, November 19
 
Computer Science/Discrete Mathematics Seminar I
Topic:                    A Complete Dichotomy Rises from the Capture of
Vanishing Signatures
Speaker:               Jin-Yi Cai, University of Wisconsin
Time/Room:         11:15am - 12:15pm/S-101
Abstract:               See below
 
Members Seminar
Topic:                    Univalent Foundations
Speaker:               Steve Awodey, Carnegie Mellon University; 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, November 20
 
Computer Science/Discrete Mathematics Seminar II
Topic:                    On the Complexity of Matrix Multiplication and
Other Tensors
Speaker:               Joseph Landsberg, Texas A&M University
Time/Room:         10:30am - 12:30pm/S-101
Abstract:               See below
 
Working Group on Univalent Foundations
Time/Room:         1:30pm - 2:45pm/S-101
 
 
 
Wednesday, November 21
 
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
 
Mathematical Conversations
                               There will be no Mathematical Conversations
talk today
Time/Room:         6:00pm - 7:30pm
 
 
 
Thursday, November 22
 
Univalent Foundations Seminar
                               No Talk Today -- IAS Closed for Thanksgiving
Holiday
Time/Room:         11:00am - 12:30pm
 
Working Group on Algebraic Number Theory
                               No meeting today -- IAS closed for
Thanksgiving Holiday
Time/Room:         2:00pm - 4:00pm
 
Joint IAS/PU Number Theory Seminar
                               No Talk Today -- IAS Closed for Thanksgiving
Holiday
Time/Room:         4:30pm - 5:30pm
 
 
 
Friday, November 23
 
Working Group on Univalent Foundations
                               No Meeting Today -- IAS Closed for
Thanksgiving Holiday
Time/Room:         11:00am - 12:30pm/S-101
 
Joint IAS-PU Symplectic Geometry Seminar
                               No Talk Today -- IAS Closed for Thanksgiving
Holiday
Time/Room:         4:30pm - 5:30pm/S-101
 
 
 
1             A Complete Dichotomy Rises from the Capture of Vanishing
Signatures
               Jin-Yi Cai
 
Holant Problems are a broad framework to describe counting problems. The
framework generalizes
counting Constraint Satisfaction Problems and partition functions of Graph
Homomorphisms.
We prove a complexity dichotomy theorem for Holant problems over an
arbitrary set of complex-valued
symmetric constraint functions $\mathcal{F}$, also called signatures, on
Boolean variables. This
extends and unifies all previous dichotomies for Holant problems on
symmetric signatures (taking
values without a finite modulus).
 
The dichotomy theorem has an explicit tractability criterion.
A Holant problem defined by $\mathcal{F}$ is solvable in polynomial time if
it satisfies this
tractability criterion, and is \#P-hard otherwise.
The proof of this theorem utilizes many previous dichotomy theorems on
Holant problems and Boolean
\#CSP. Holographic transformations play an indispensable role, not only as a
proof technique, but
also in the statement of the dichotomy criterion.
 
 
 
 
 
2             Univalent Foundations
               Steve Awodey
 
This talk is intended for a general audience. The recent discovery of an
interpretation of
constructive type theory into abstract homotopy theory has led to a new
approach to foundations with
both intrinsic geometric content and a computational implementation. In this
setting, Vladimir
Voevodsky has proposed new axiom for foundations with both geometric and
logical significance: the
Univalence Axiom. It captures formally a familiar practice of modern
mathematics, namely the
informal identification of isomorphic objects. Although UA is incompatible
with conventional
foundations, it is a powerful addition to homotopy type theory and forms the
basis of the new
Univalent Foundations Program. In this talk, I will explain homotopy type
theory and the Univalence
Axiom.
 
 
 
 
3             On the Complexity of Matrix Multiplication and Other Tensors
               Joseph Landsberg
 
Many problems from complexity theory can be phrased in terms of tensors. I
will begin by reviewing
basic properties of tensors and discussing several measures of the
complexity of a tensor. I'll then
focus on the complexity of matrix multiplication. Since March 2012 there
have been significant
advances in our understanding of the complexity of matrix multiplication.
This progress was made
possible via tools from algebraic geometry and representation theory, and
I'll explain why such
techniques are useful without assuming any prior background in them.
 
 
 
IAS Math Seminars Home Page:






http://www.math.ias.edu/seminars

 

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