Seminars and Colloquia by Series

An Algebraic Approach to Network Optimization

Series
Algebra Seminar
Time
Monday, November 11, 2013 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Sanjeevi Krishnan – University of Pennsylvania –

Please Note: This talk assumes no familiarity with directed topology, flow-cut dualities, or sheaf (co)homology.

Flow-cut dualities in network optimization bear a resemblance to topological dualities. Flows are homological in nature, cuts are cohomological in nature, constraints are sheaf-theoretic in nature, and the duality between max flow-values and min cut-values (MFMC) resembles a Poincare Duality. In this talk, we formalize that resemblance by generalizing Abelian sheaf (co)homology for sheaves of semimodules on directed spaces (e.g. directed graphs). Such directed (co)homology theories generalize constrained flows, characterize cuts, and lift MFMC dualities to a directed Poincare Duality. In the process, we can relate the tractability and decomposability of generalized flows to local and global flatness conditions on the sheaf, extending previous work on monoid-valued flows in the literature [Freize].

Colmez's product formula for CM abelian varieties.

Series
Algebra Seminar
Time
Monday, November 11, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Andrew Obus – University of Virginia
We complete a proof of Colmez, showing that the standard product formula for algebraic numbers has an analog for periods of CM abelian varieties with CM by an abelian extension of the rationals. The proof depends on explicit computations with the De Rham cohomology of Fermat curves, which in turn depends on explicit computation of their stable reductions.

Colored Jones polynomials and double affine Hecke algebras

Series
Geometry Topology Seminar
Time
Monday, November 11, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Peter Samuelson – University of Toronto
Frohman and Gelca showed that the Kauffman bracket skein module of the thickened torus is the Z_2 invariant subalgebra A'_q of the quantum torus A_q. This shows that the Kauffman bracket skein module of a knot complement is a module over A'_q. We discuss a conjecture that this module is naturally a module over the double affine Hecke algebra H, which is a 3-parameter family of algebras which specializes to A'_q. We give some evidence for this conjecture and then discuss some corollaries. If time permits we will also discuss a related topological construction of a 2-parameter family of H-modules associated to a knot in S^3. (All results in this talk are joint with Yuri Berest.)

Southeast Geometry Seminar XXIII

Series
Other Talks
Time
Sunday, November 10, 2013 - 08:45 for 8 hours (full day)
Location
Emory University
Speaker
Southeast Geometry Seminar – Emory University
The Southeast Geometry Seminar is a series of semiannual one-day events focusing on geometric analysis. These events are hosted in rotation by the following institutions: Emory University; Georgia Institute of Technology; University of Alabama at Birmingham; University of Tennessee Knoxville. The following five speakers will give presentations: Alex Freire (University of Tennessee, Knoxville); Matthew Gursky (University of Notre Dame); William Minicozzi II (MIT); Yanir Rubinstein (University of Maryland); Gaoyong Zhang (NYU-Poly). Please email oliker@mathcs.emory.edu if you plan to attend and wish to request support.

All finite groups are involved in the mapping class group

Series
Geometry Topology Seminar
Time
Friday, November 8, 2013 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
G. Masbaum – Institut de Mathématiques de Jussieu
Let g be a positive integer and let Gamma_g be the mapping class group of the genus g closed orientable surface. We show that every finite group is involved in Gamma_g. (Here a group G is said to be involved in a group Gamma if G is isomorphic to a quotient of a subgroup of Gamma of finite index.) This answers a question asked by U. Hamenstadt. The proof uses quantum representations of mapping class groups. (Joint work with A. Reid.)

Forbidden Vertices

Series
ACO Student Seminar
Time
Friday, November 8, 2013 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Gustavo Angulo – ISyE, Georgia Tech
In this talk, we introduce and study the forbidden-vertices problem. Given a polytope P and a subset X of its vertices, we study the complexity of linear optimization over the subset of vertices of P that are not contained in X. This problem is closely related to finding the k-best basic solutions to a linear problem. We show that the complexity of the problem changes significantly depending on how both P and X are described, that is, on the encoding of the input data. For example, we analyze the case where the complete linear formulation of P is provided, as opposed to the case where P is given by an implicit description (to be defined in the talk). When P has binary vertices only, we provide additional tractability results and linear formulations of polynomial size. Some applications and extensions to integral polytopes will be discussed. Joint work with Shabbir Ahmed, Santanu S. Dey, and Volker Kaibel.

The 2-core of a Random Inhomogeneous Hypergraph

Series
Stochastics Seminar
Time
Thursday, November 7, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Omar Abuzzahab – Georgia Tech
The 2-core of a hypergraph is the unique subgraph where all vertices have degree at least 2 and which is the maximal induced subgraph with this property. This talk will be about the investigation of the 2-core for a particular random hypergraph model --- a model which differs from the usual random uniform hypergraph in that the vertex degrees are not identically distributed. For this model the main result proved is that as the size of the vertex set, n, tends to infinity then the number of hyperedges in the 2-core obeys a limit law, and this limit exhibits a threshold where the number of hyperedges in the 2-core transitions from o(n) to Theta(n). We will discuss aspects of the ideas involved and discuss the background motivation for the hypergraph model: factoring random integers into primes.

On Higher-Dimensional Oscillation in Ergodic Theory

Series
Analysis Seminar
Time
Wednesday, November 6, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ben Krause – UCLA
We will discuss the fine notion of the pointwise convergence of ergodic averages in setting where one the ergodic transformation is a Z^d action, and the averages are over more exotic sets than just cubes. In this setting, pointwise convergence does not follow from the usual ergodicity arguments. Bourgain, in his study of the polynomial ergodic averages invented the variational technique, which we extend to our more exotic averages.

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