Seminars and Colloquia by Series

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)

Multiscale Crystal Plasticity Modeling for Metals

Series
GT-MAP Seminar
Time
Friday, December 2, 2016 - 15:00 for 2 hours
Location
Skiles 006
Speaker
Prof. David McDowell and Shouzhi Xu – GT ME and MSE

Please Note: Talk by Shuozhi Xu, Title: Algorithms and Implementation for the Concurrent Atomistic-Continuum Method. Abstract: Unlikemany other multiscale methods, the concurrent atomistic-continuum (CAC) method admits the migration of dislocations and intrinsic stacking faults through a lattice while employing an underlying interatomic potential as the only constitutive relation. Here, we build algorithms and develop a new CAC code which runs in parallel using MPI with a domain decomposition algorithm. New features of the code include, but are not limited to: (i) both dynamic and quasistatic CAC simulations are available, (ii) mesh refinement schemes for both dynamic fracture and curved dislocation migration are implemented, and (iii) integration points in individual finite elements are shared among multiple processors to minimize the amount of data communication. The CAC program is then employed to study a series of metal plasticity problems in which both dislocation core effects at the nanoscale and the long range stress field of dislocations at the submicron scales are preserved. Applications using the new code include dislocation multiplication from Frank-Read sources, dislocation/void interactions, and dislocation/grain boundary interactions.

Crystal plasticity modeling is useful for considering the influence of anisotropy of elastic and plastic deformation on local and global responses in crystals and polycrystals. Modern crystal plasticity has numerous manifestations, including bottom-up models based on adaptive quasi-continuum and concurrent atomistic-continuum methods in addition to discrete dislocation dynamics and continuum crystal plasticity. Some key gaps in mesoscale crystal plasticity models will be discussed, including interface slip transfer, grain subdivision in large deformation, shock wave propagation in heterogeneous polycrystals, and dislocation dynamics with explicit treatment of waves. Given the mesoscopic character of these phenomena, contrasts are drawn between bottom-up (e.g., atomistic and discrete dislocation simulations and in situ experimental observations) and top-down (e.g., experimental) information in assembling mesoscale constitutive relations and informing their parameters.

The universal quantum invariant and colored ideal triangulations

Series
Geometry Topology Seminar
Time
Friday, December 2, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
S. Suzuki – RIMS, Kyoto University
The Drinfeld double of a finite dimensional Hopf algebra is a quasi-triangular Hopf algebra with the canonical element as the universal R matrix, and we obtain a ribbon Hopf algebra by adding the ribbon element. The universal quantum invariant is an invariant of framed links, and is constructed diagrammatically using a ribbon Hopf algebra. In that construction, a copy of the universal R matrix is attached to each positive crossing, and invariance under the Reidemeister III move is shown by the quantum Yang-Baxter equation of the universal R matrix. On the other hand, R. Kashaev showed that the Heisenberg double has the canonical element (the universal S matrix) satisfying the pentagon relation. In this talk we reconstruct the universal quantum invariant using Heisenberg double, and extend it to an invariant of colored ideal triangulations of the complement. In this construction, a copy of the universal S matrix is attached to each tetrahedron and the invariance under the colored Pachner (2,3) move is shown by the pentagon equation of the universal S matrix

Lazifying Conditional Gradient Algorithms

Series
ACO Student Seminar
Time
Friday, December 2, 2016 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel Zink – Georgia Tech
Conditional gradient algorithms (also often called Frank-Wolfe algorithms) are popular due to their simplicity of only requiring a linear optimization oracle and more recently they also gained significant traction for online learning. While simple in principle, in many cases the actual implementation of the linear optimization oracle is costly. We show a general method to lazify various conditional gradient algorithms, which in actual computations leads to several orders of magnitude of speedup in wall-clock time. This is achieved by using a faster separation oracle instead of a linear optimization oracle, relying only on few linear optimization oracle calls.

Asymptotic equivalence between density estimation and Gaussian white noise revisited

Series
Job Candidate Talk
Time
Thursday, December 1, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Kolyan Ray – Leiden Univ. –
Asymptotic equivalence between two statistical models means that they have the same asymptotic (large sample) properties with respect to all decision problems with bounded loss. In nonparametric (infinite-dimensional) statistical models, asymptotic equivalence has been found to be useful since it can allow one to derive certain results by studying simpler models. One of the key results in this area is Nussbaum’s theorem, which states that nonparametric density estimation is asymptotically equivalent to a Gaussian shift model, provided that the densities are smooth enough and uniformly bounded away from zero.We will review the notion of asymptotic equivalence and existing results, before presenting recent work on the extent to which one can relax the assumption of being bounded away from zero. We further derive the optimal (Le Cam) distance between these models, which quantifies how close they are for finite-samples. As an application, we also consider Poisson intensity estimation with low count data. This is joint work with Johannes Schmidt-Hieber.

Pages