**Seminars and Colloquiums**

for the week of January 25, 2016

for the week of January 25, 2016

*SPEAKER:*

Shashikant Mulay, UTK, Monday

Jim Conant, UTK, Monday

Panel on UG Research Opportunities in Math, Thursday

Stefan Richter, UTK, Friday

David Zureick-Brown, Emory, Friday

*TEA TIME
3:00 – 3:30 pm, Ayres 401
Monday, Tuesday, & Wednesday
Hosted by Nate Pollesch*

**Monday, January 25th**

ALGEBRA SEMINAR

TITLE: Organizational Meeting

SPEAKER: Shashikant Mulay, UTK

TIME: 3:35pm - 4:25pm

ROOM: Ayres 114

I have created a google sheet for scheduling talks of visitors as well as locals ... as soon as an outside visitor finalizes their visit plan, please put their name in at the date they speak.

TOPOLOGY AND GEOMETRY SEMINAR

TITLE: Organizational Meeting

SPEAKER: Jim Conant, UTK

TIME: 2:30pm – 3:20pm

ROOM: Ayres 113

** Thursday, January 28th **

JUNIOR COLLOQUIUM

TITLE: Panel on UG Research Opportunities in Math

TIME: 3:00pm - 4:00pm (Note: Regular time (3:40p – 4:35p) will resume at next Junior Colloquium)

ROOM: Ayres 405

In this JC, a panel of students and professors will be available to discuss research opportunities in mathematics. Students with research experience in various fields including mathematical biology, algebra, and topology will take part in the panel, as well as faculty members with experience mentoring undergraduate research projects. Members of the panel include Dr. Lenhart, Virgina Parkman, Chris Loa, and Adam LaClair. If you have any questions about undergraduate research and REU opportunities in mathematics, then this is a great place to get started.

** Friday, January 29th**

ANALYSIS SEMINAR

TITLE: Functions as quotients of multipliers

SPEAKER: Stefan Richter

TIME: 2:30pm - 3:20pm

ROOM: Ayres 121

It follows from a classical theorem of F. Riesz that every function in the Hardy space H^2 can be written as a quotient of two bounded analytic functions. I will discuss analogues of this result in spaces other than H^2.

ALGEBRA SEMINAR

TITLE: Graded rings of modular forms and canonical rings of stacky curves.

SPEAKER: David Zureick-Brown, Emory

TIME: 1:25pm-2:15pm

ROOM: TBA

We give a generalization to stacks of the classical theorem of Petri -- i.e., we give a presentation for the canonical ring of a stacky curve. This is motivated by the following application: we give an explicit presentation for the ring of modular forms for a Fuchsian group with cofinite area, which depends on the signature of the group. This is joint work with John Voight.

COLLOQUIUM

TITLE: Diophantine and tropical geometry

SPEAKER: David Zureick-Brown, Emory

TIME: 3:35pm-4:25pm, Friday Jan 29

ROOM: Ayres 405

Diophantine geometry is the study of integral solutions to a polynomial equation. For instance, for integers a,b,c >= 2 satisfying 1/a + 1/b + 1/c < 1, Darmon and Granville proved that the individual generalized Fermat equation x^a + y^b = z^c has only finitely many coprime integer solutions. Conjecturally something stronger is true: for a,b,c >= 3 there are no non-trivial solutions.

I'll discuss various other Diophantine problems, with a focus on the underlying intuition and conjectural framework. I will especially focus on the uniformity conjecture, and will explain new ideas from tropical geometry and our recent partial proof of the uniformity conjecture.

*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:**