Usual time: Thursday 4-5pm in the Halkin Room (6402).
Organiser: Justin Roberts
Oct 4:
Oct 8 (Monday): Dick Gross (Harvard) Parameters of Discrete
Series Representations
Oct 11:
Oct 18: Pan Peng (Harvard) On a proof of the
Labastida-Marino-Ooguri-Vafa conjecture.
Based on large N Chern-Simons/topological string duality, in
a series of papers, J.M.F. Labastida, M. Marino, H. Ooguri and C. Vafa
conjectured certain remarkable new algebraic structure of link
invariants and the existence of infinite series of new integer
invariants. In this lecture, I will describe a proof of this
conjecture. Moreover, I will show that these new integer invariants
vanish at large genera. In the end of the talk, some application in the
knot theory and related problems (e.g., the famous volume conjecture),
will also be discussed.
Oct 25:
Nov 1:
Nov 8:
Nov 13 (Tuesday): Natalia Berloff
Nov 15: Herbert Heyer
Nov 22: Thanksgiving!
Nov 29: Harm Derksen (Michigan)
Dec 6: G. Kyriazis (Cyprus and U. South Carolina)i
At the start of January there will be lots of visitors because of the
AMS conference! Here are some of them:
Tues Jan 8, 4pm: Manfred Kolster Special values of zeta
functions
Thurs Jan 10, 11am: Sasha Voronov (Minnesota) The n-category of
cobordisms and TQFT
Since Atiyah and Segal described the
notions of Topological Quantum Field Theory (TQFT) and Conformal Field
Theory (CFT), mathematicians have been looking for a suitable
n-category framework to describe cobordisms with corners and a more
general TQFT involving such cobordisms as a functor from that higher
category of cobordisms with corners to a higher category of vector
spaces. The problem deals with such standard difficulties of higher
category theory as weak vs. strict axioms, coherence, suitable
diagrams, etc.: almost every higher category theorist has this problem
in the back of her head, but nobody seems to have gotten through to a
satisfactory solution. In the talk, I will describe the set up Mark
Feshbach and I have found.
Thurs Jan 10, 4pm: Craig Westerland (Wisconsin) Hurwitz spaces and
string topology
String topology, originating in the work of
Chas and Sullivan in the late 90's, concerns itself with the algebraic
and topological properties of loop spaces of manifolds. Many
interesting connections to representation theory and symplectic
geometry have recently been established. Hurwitz spaces are moduli
spaces of branched covers of Riemann surfaces. In this talk we will
propose a generalization of this notion that serves as a bridge
between the two subjects, and allows for the construction of
operations in string topology governed by the moduli spaces of Riemann
surfaces.
Fri Jan 11, 2pm: Matt Hedden Symplectic geometry and
invariants for low-dimensional topology
Monday Jan 14, 4pm: Angela Gibney Mori cones of
algebraic varieties
The Mori cone is a fundamental, often elusive, invariant
of an algebraic variety and is the central object of study in higher
dimensional algebraic geometry. In this talk I will explain Fulton's
conjecture, which predicts a very simple description of the Mori cone
of the moduli space of curves. I'll show how one can naturally obtain
upper and lower bounds for the Mori cone of a large class of
varieties. In the case of the moduli space of curves, the upper
bound is the cone described by Fulton's conjecture. In particular,
this gives a new possibitlity for the Mori cone and a new perspective
on Fulton's conjecture.
Wednesday Jan 16, 4pm: Danny Krashen The u-invariant of fields
The u-invariant of a field is defined to be the maximal
dimension (number of variables) of a quadratic form which has no
nontrivial zeros. Although there are some expectations for what
u-invariants should be of most "naturally occuring" fields, these
invariants are unknown in a great number of situations. For example,
if $F$ is a nonreal number field, it is known that $u(F) = 4$, and it
is expected that the u-invariant of the rational function field $F(t)$
should be $8$. At this point, however, there is no known bound for
$u(F(t))$ (and no proof it is even finite).
Important progress on this type of problem was obtained by Parimala
and Suresh late last year, who showed that the u-invariant of a
rational function field $F(t)$ is $8$ when $F$ is $p$-adic ($p$ odd).
In this talk I
will describe joint work with David Harbater and Julia Hartmann
in which we give an independent proof and a generalization of this
result using the method of "field patching."
Thursday Jan 17, 4pm: Dragos Oprea
Thursday Jan 24, 4pm: Soumik Pal
Thursday Jan 31, 4pm: Dimitris Gatzouras
Thursday Feb 21, 4pm: Sasha Razborov
Tuesday Feb 19, 4pm: Ezra MillerMetric geometry and
unfoldings of polyhedra
Most of us as children saw those paper or cardboard cutouts,
which we could call "foldouts", whose edges glue to form
(boundaries of) 3-dimensional convex polyhedra. Just how did
anyone figure out how to make them? Given a 3-dimensional
convex polyhedron, does there always exist a foldout in the
plane? What about higher dimensions? These questions have
surprising answers, depending on the precise meaning of
"foldout". One method is to treat boundaries of polyhedra like
Riemannian manifolds. Algorithmic concerns then raise
fundamental issues of computational complexity for the
combinatorics of geodesics on polyhedra. This talk is on joint
work with Igor Pak.
Tuesday Feb 26th, 4pm: Yongbin Ruan
Tues April 8th: Juan Luis Vazquez
Thurs April 10th: Bernhard Palsson (UCSD bioeng) New
'Dimensions' in Genome Annotation
Traditional Genome annotation involves the enumeration of open reading
frames and their functional assignment. Currently, there are on-going
efforts to identify all the interactions between these components.
The resulting map of interactions effectively represents a 2D
annotation. It takes the form of a stoichiometric matrix, if the
interactions are described with chemical equations. The formulation
and properties of this matrix are detailed and how it can be used as
the basis for computing allowable phenotypic functions. The issues
associated with the packing of the bacterial genome and the function
of the interaction map in 3D will also be discussed. Finally, we will
go over the issue of genomes changing in space and time (4D) through
adaptive evolution and describe the full re-sequencing of bacterial
genomes to map all genetic changes that occur during adaptation. All
of these efforts represent mathematical challenges.
Tues April 15th, 4pm: Allen Knutson Totally nonnegative
matrices, juggling patterns, and the affine flag manifold
Consider $b\times n$ real matrices such that every $b\times b$ minor
has nonnegative determinant. Since there are polynomial relations between
these minors, not every pattern of zero vs. strictly positive is
achievable. In a widely circulated prepreprint, Alex Postnikov
gave many ways to index the patterns that are.
I'll describe a new indexing, by ``bounded juggling patterns'',
which will require a brief foray into the mathematics of juggling
(with demonstrations). It turns out that many of the natural concepts
from the matrix picture have been known to jugglers for 20 years.
Unbounded juggling patterns form a group, the affine Weyl group, and
thereby index the Schubert varieties on the (infinite-dimensional)
affine flag manifold. I'll explain how the complicated finite-dimensional
geometry of Postnikov's stratification is induced from what is
actually much more familiar infinite-dimensional geometry.
Thurs April 17th, 4pm: Assaf Naor
Tuesday April 22nd, 4pm: Bill Casselman Patterns in Coxeter
groups
Thurs April 24th: Mia Minnes
Thurs May 8th: Herbert Levine (UCSD physics)
Thurs May 22nd: ? (Philip Gill)
Thurs May 29th: Alexandru Buium (UNM)
Thurs June 5th: AWM
Dan Klain?
Nathan Habegger, Tues May 6, 4pm? (have abstract)
justin@math.ucsd.edu
