Seminars and Colloquia by Series

Existence conditions for permanental and multivariate negative binomial distributions

Series
Stochastics Seminar
Time
Monday, January 9, 2017 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Franck Maunoury – Université Pierre et Marie Curie
We consider permanental and multivariate negative binomial distributions. We give sim- ple necessary and sufficient conditions on their kernel for infinite divisibility, without symmetry hypothesis. For existence of permanental distributions, conditions had been given by Kogan and Marcus in the case of a 3 × 3 matrix kernel: they had showed that such distributions exist only for two types of kernels (up to diagonal similarity): symmet- ric positive-definite matrices and inverse M-matrices. They asked whether there existed other classes of kernels in dimensions higher than 3. We give an affirmative answer to this question, by exhibiting (in any finite dimension higher than 3) a family of matrices which are kernels of permanental distributions but are neither symmetric, nor inverse M-matrices (up to diagonal similarity). Analog properties (by replacing inverse M-matrices by entrywise non-negative matrices) are given for multivariate negative binomial distribu- tions. These notions are also linked with the study of inverse power series of determinant. This is a joint work with N. Eisenbaum.

Cosmetic surgeries on homology spheres

Series
Geometry Topology Seminar
Time
Monday, January 9, 2017 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Huygens Ravelomanana – University of Georgia
Dehn surgery is a fundamental tool for constructing oriented 3-Manifolds. If we fix a knot K in an oriented 3-manifold Y and do surgeries with distinct slopes r and s, we can ask under which conditions the resulting oriented manifold Y(r) and Y(s) might be orientation preserving homeomorphic. The cosmetic surgery conjecture state that if the knot exterior is boundary irreducible then this can't happen. My talk will be about the case where Y is an homology sphere and K is an hyperbolic knot.

Numerical Algebraic Geometry adjoint meeting

Series
Other Talks
Time
Sunday, January 8, 2017 - 09:00 for 8 hours (full day)
Location
Skiles 005
Speaker
Anton Leykin – Georgia Tech –

Please Note: Tentative schedule: 9-12: mini-presentations, informal discussion, Q&A, led by Jose Rodriguez (numerical decomposition), Elizabeth Gross (reaction networks), Dan Bates (numerical AG for sciences and engineering); 12-1: lunch; 1pm+: catch flights, continue talking in groups.

This is an informal get-together of the Joint Meetings participants and locals interested in various aspects of Numerical Algebraic Geometry. This area combines numerical analysis and nonlinear algebra in algorithms that found various applications in other parts of mathematics and outside. (If interested in joining, email leykin@math.gatech.edu)

More Tales of our Forefathers

Series
School of Mathematics Colloquium
Time
Tuesday, January 3, 2017 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Barry Simon – California Institute of Technology
This is not a mathematics talk but it is a talk for mathematicians. Too often, we think of historical mathematicians as only names assigned to theorems. With vignettes and anecdotes, I'll convince you they were also human beings and that, as the Chinese say, "May you live in interesting times" really is a curse. More tales following up on the talk I gave at GaTech in Nov., 2013. It is not assumed listeners heard that earlier talk.

Multiple q-Meixner polynomials of the first kind

Series
Analysis Seminar
Time
Friday, December 16, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Jorge Arvesu Carballo – Universida Carlos III de Madrid –
I will present a discrete family of multiple orthogonal polynomials defined by a set of orthogonality conditions over a non-uniform lattice with respect to different q-analogues of Pascal distributions. I will obtain some algebraic properties for these polynomials (q-difference equation and recurrence relation, among others) aimed to discuss a connection with an infinite Lie algebra realized in terms of the creation and annihilation operators for a collection of independent ascillators. Moreover, if time allows, some vector equilibrium problem with constraint for the nth root asymptotics of these multiple orthogonal polynomials will be discussed.

The Cubical Route to Understanding Groups

Series
School of Mathematics Colloquium
Time
Friday, December 9, 2016 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel Wise – McGill University
Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that have recently culminated in the resolution of the virtual Haken conjecture for 3-manifolds, and simultaneously dramatically extended our understanding of many infinite groups.

Conductors and minimal discriminants of hyperelliptic curves with rational Weierstrass points

Series
Algebra Seminar
Time
Monday, December 5, 2016 - 16:15 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Padma Srinivasan – Georgia Tech
Conductors and minimal discriminants are two measures of degeneracy of the singular fiber in a family of hyperelliptic curves. In the case of elliptic curves, the Ogg-Saito formula shows that (the negative of) the Artin conductor equals the minimal discriminant. In the case of genus two curves, equality no longer holds in general, but the two invariants are related by an inequality. We investigate the relation between these two invariants for hyperelliptic curves of arbitrary genus.

Polynomial functors and algebraic K-theory

Series
Geometry Topology Seminar
Time
Monday, December 5, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Akhil Mathew – Harvard University
The Grothendieck group K_0 of a commutative ring is well-known to be a \lambda-ring: although the exterior powers are non-additive, they induce maps on K_0 satisfying various universal identities. The \lambda-operations are known to give homomorphisms on higher K-groups. In joint work in progress with Barwick, Glasman, and Nikolaus, we give a general framework for such operations. Namely, we show that the K-theory space is naturally functorial with respect to polynomial functors, and describe a universal property of the extended K-theory functor. This extends an earlier algebraic result of Dold for K_0.

Discrete geometry and representation theory

Series
Combinatorics Seminar
Time
Friday, December 2, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ben Steinberg – CUNY
One can associate regular cell complexes to various objects from discrete and combinatorial geometry such as real and complex hyperplane arrangements, oriented matroids and CAT(0) cube complexes. The faces of these cell complexes have a natural algebraic structure. In a seminal paper from 1998, Bidigare, Hanlon and Rockmore exploited this algebraic structure to model a number of interesting Markov chains including the riffle shuffle and the top-to-random shuffle, as well as the Tsetlin library. Using the representation theory of the associated algebras, they gave a complete description of the spectrum of the transition matrix of the Markov chain. Diaconis and Brown proved further results on mixing times and diagonalizability for these Markov chains. Bidigare also noticed in his thesis a natural connection between Solomon's descent algebra for a finite Coxeter group and the algebra associated to its Coxeter arrangement. Given, the nice interplay between the geometry, the combinatorics and the algebra that appeared in these two contexts, it is natural to study the representation theory of these algebras from the point of view of the representation theory of finite dimensional algebras. Building on earlier work of Brown's student, Saliola, for the case of real central hyperplane arrangements, we provide a quiver presentation for the algebras associated to hyperplane arrangements, oriented matroids and CAT(0) cube complexes and prove that these algebras are Koszul duals of incidence algebras of associated posets. Key to obtaining these results is a description of the minimal projective resolutions of the simple modules in terms of the cellular chain complexes of the corresponding cell complexes.This is joint work with Stuart Margolis (Bar-Ilan) and Franco Saliola (University of Quebec at Montreal)

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