## Colloquium

##### 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 ...
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#### 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, ...
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### 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 ...
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#### 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 ...
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### Thursday, 29 January 2015

#### Colloquium

*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 ...
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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 ...
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#### 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. ...
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#### 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 ...
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