**Seminars and Colloquiums**

for the week of February 27, 2017

for the week of February 27, 2017

*SPEAKER:*

Dhruv Ranganathan, MIT , Monday

Jeremy Siegert, UTK, Monday

Joshua Mike, UTK, Tuesday

Remus Nicoara, UTK, Wednesday

Richard Schwartz, Professor at Brown University, Thursday

Richard Schwartz, Professor at Brown University, Friday

*TEA TIME -
3:00 pm – 3:30 pm
Monday & Tuesday Room: Ayres 401
Tuesday & Wednesday; Room: Ayres 4th Floor Common Area*

*Hosted by:*

*Mahir Demir and Mustafa Elmas*

** Monday, February 27th **

ALGEBRA SEMINAR

TITLE: A Brill-Noether theorem for curves of a fixed gonality

SPEAKER: Dhruv Ranganathan, MIT

TIME: 2:30pm – 3:20pm

ROOM: Ayres 111

The Brill-Noether varieties of a curve C parametrize embeddings of C of prescribed degree into a projective space of prescribed dimension. When C is general in moduli, these varieties are well understood: they are smooth, irreducible, and have the "expected" dimension. As one ventures deeper into the space of curves, past the locus of general curves, these varieties exhibit intricate, even pathological, behaviour: they can be highly singular and their dimensions are unknown. A first measure of the failure of a curve to be general is its gonality. I will present a generalization of the Brill-Noether theorem, which determines the dimensions of the Brill-Noether varieties on a general curve of fixed gonality, i.e. "general inside a chosen special locus". The proof blends a study of Berkovich skeletons of maps from curves to toric varieties with tropical linear series theory. The deformation theory of logarithmic stable maps acts as the bridge between these ideas. This is joint work with Dave Jensen.

TOPOLOGY/GEOMETRY SEMINAR

TITLE: Topics in coarse geometry: metrizability and Higson corona

SPEAKER: Jeremy Siegert, UTK

TIME: 2:30-3:20PM

ROOM: Ayres Hall 113

** Tuesday, February 28**

PROBABLITY SEMINAR

TITLE: Constructing Distributions of Persistence Diagrams: Part II

SPEAKER: Josh Mike, UTK

TIME: 2:10pm – 3:25pm

ROOM: Ayres 113

In Part I, we began with background on the pipeline of persistent homology for point cloud data, including filtrations of simplicial complexes and describing how to build persistence diagrams from the filtration. Examples were provided to motivate use in data analysis. We concluded by discussing some issues with constructing distributions of persistence diagrams.

Now we will introduce the theory of finite random sets as a framework within which to define distributions of persistence diagrams. We will construct a kernel distribution centered at a fixed persistence diagram and give a closed form for its probability density function. A few properties of this construction will be presented and future directions will be discussed. This ongoing work is joint with Vasileios Maroulas.

**Wednesday, March 1st **

ANALYSIS SEMINAR

TITLE:
Analytic deformations of commuting squares, Part 2

SPEAKER:
Dr. Remus Nicoara, UTK

TIME:
2:30pm-3:20pm

ROOM:
Ayres 113

Finite groups, and more generally finite dimensional Hopf C*-algebras, can be encoded in S.Popa’s commuting squares and thus used as construction data for V.Jones’ subfactors. We construct analytic deformations of such commuting squares, and present consequences to the theory of complex Hadamard matrices and the theory of subfactors.

** Thursday, March 2nd **

JR. COLLOQUIUM

TITLE: Piecewise isometric maps

SPEAKER: Richard Schwartz, Professor at Brown University

TIME: 3:40pm – 4:30pm

ROOM: Ayres 405

I will explain maps which are based on the idea of cutting a polygon (or the plane) apart into smaller pieces and moving each piece around by isometries. These maps, when treated as dynamical systems, often produce beautiful and intricate pictures. I'll give some examples of these maps and show pictures of what they do.

** Friday, March 3rd **

COLLOQUIUM

TITLE:
5 points on a sphere

SPEAKER:
Richard Schwartz, Professor at Brown University

TIME:
3:35pm-4:30pm

ROOM:
Ayres 405

For a long time, people have studied how to place N points on the sphere so as to minimize the energy potential of the configuration. The classical case, known as Thomson's problem, concerns the electrostatic (or 1/r) potential, but people often consider powerlaw (1/r^s) potentials. For the cases N=2,3,4,6,12, the answer is well-known, and independent of the power law. I will explain my recent results for the case N=5, which show that the triangular-bi-pyramid is the minimizer for a power law potential if and only if the exponent lies in the interval (0,S] where S=15.048...is some kind of phase transition constant. My talk will feature some nice computer demos and a discussion of the nature of computer-assisted proofs.

*If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar. *

*If you have questions, or a date you would like to confirm, please contact colloquium AT math DOT utk DOT edu *

**Past notices:**

Winter Break