Week of 25 January 2015 Mathematics Seminars



Higgs bundles, spectral data, and applications

Thursday, January 29, 2015 at 3:30p.m.
Laura Schaposnik (University of Illinois at Urbana-Champaign)
Abstract: A Higgs bundle (introduced by N. Hitchin in 1987) is a pair of a holomorphic vector bundle and a holomorphic 1-form taking values in the endomorphisms of the bundle. The moduli space of Higgs bundles carries a natural Hyperkähler structure, through which we can study Lagrangian subspaces (A-branes) or holomorphic subspaces (B-branes) with respect to each structure. Notably, these A and B-branes have gained significant attention in string theory. We shall begin the talk by first introducing Higgs bundles for complex Lie groups and the associated Hitchin fibration, and recalling how to realize Langlands duality through spectral data. We shall then look at a natural construction of families of subspaces which give different types of branes. Finally, by means of spectral data, we shall relate these branes to the study of 3-manifolds, surface group representations. We shall conclude with some conjectures related to Langlands duality.

Monday, 26 January 2015

Topology Seminar

Algebraic invariants of singularities at 2:30p.m. in VinH 570
Christian Haesemeyer  (UCLA)
I will discuss my work with Cortinas, Walker, Weibel on the K-theory and cyclic homology of singular algebraic varieties from the point of view of ... ( more )

Automorphic Forms and Number Theory

Varying qualities of compact operators on spaces of automorphic forms at 3:35p.m. in VinH 364
Paul Garrett

Tuesday, 27 January 2015

Geometric Analysis Learning Seminar

Eigenvalues of Laplacian and multi-way isoperimetric constants on weighted Riemannian manifolds at 10:00a.m. in VinH 364
Pak Yeung Chan  (U of M mathematics Department)

Climate Seminar

Hopf bifurcation for Welander's piecewise smooth model of ocean circulation at 11:15a.m. in VinH 570
Professor Richard McGehee  (U of M Mathematics)

Combinatorics Seminar

Multiplex juggling probabilities at 1:25p.m. in Vincent Hall 570
Jang Soo Kim  (SKKU)
Imagine that a juggler is juggling balls. Let's assume that he catches and throws at most one ball at each discrete beat. At each beat, ... ( more )

Wednesday, 28 January 2015

Math Physics Seminar

Involutive bases and PDEs at 12:20p.m. in VinH 570
Orn Arnaldsson  (University of Minnesota)
Deciding whether a system of differential equations is formally integrable (i.e. has no integrability conditions) is a hard problem and as of yet no general ... ( more )

PDE Seminar

Loss of continuity of the solution map for the Euler equations, and single exponential bound of the vorticity gradient for the two-dimensional Euler flow around a corner at 3:35p.m. in VinH 364
Joint Talk by Tsuyoshi Yoneda and Tsubasa Itoh  (Tokyo Institute of Technology)
This talk is composed by two topics about the Euler flow. In the first talk we prove that the data-to-solution map for the incompressible Euler ... ( more )

Thursday, 29 January 2015


Higgs bundles, spectral data, and applications at 3:30p.m. in Vin H 16
Laura Schaposnik  (University of Illinois at Urbana-Champaign)
A Higgs bundle (introduced by N. Hitchin in 1987) is a pair of a holomorphic vector bundle and a holomorphic 1-form taking values in the ... ( more )

Friday, 30 January 2015

Probability Seminar

Statistical properties of eigenvalues of Laplace-Beltrami operators at 2:30p.m. in VinH 311
Tiefeng Jiang  (U of M)
We study the eigenvalues of a Laplace-Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions ... ( more )

Combinatorics Seminar

Dual filtered graphs at 3:35p.m. in VinH 570
Rebecca Patrias  (UMN)
Using the Hecke insertion algorithm of Thomas and Yong as motivation, we define a K-theoretic analogue of Fomin's dual graded graphs called dual filtered graphs. ... ( more )

Math Biology Seminar

Biological models of compensatory evolution at 3:35p.m. in VinH 209
Yaniv Brandvain  (Dept. of Plant Biology, U of M)

MCFAM Seminar

What Did I Know and When Did I Know It? One Portfolio Manager's Quest for Enlightenment at 5:30p.m. in VinH 16
Mr. Scott Kovarik  (Lake Hill Capital Management LLC:http://lakehillgroup.com/)
Mr. Kovarik will spend the hour talking about the various elements of his work and what he does as a research quant, the critical qualities ... ( more )