Schedule (Last updated: 12/05/2016, 05:00 PM EST)
Note 1: because there might be a time delay for the updates on this webpage, please always first check with the Colloquium Speaker Committee for the available dates.
Note 2: Typically the colloquium talk would occur from 4-5pm in PE227, but there may be exceptions. Please check the following table for more accurate information.

Spring 2017:
Abstract:

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Fall 2016:

Date	Speaker	Affiliation	Time/Room	Talk title	Remark
09/22/2016 Thursday	Phil Harrington	University of Arkansas	4-5pm, PE 227	The Missing Riemann Mapping Theorem in Several Complex Variables
09/27/2016 Tuesday	Motohico Mulase	UC Davis	4-5pm, PE 227	What awaits us on the other side of the rainbow? A story of quantum curves and opers
10/20/2016 Thursday	Carl Cowen	Indiana University-Purdue University at Indianapolis	4-5pm, PE 227	Thoughts on Invariant Subspaces for Operators on Hilbert Spaces
11/03/2016 Thursday	Karan Singh	University of Alabama at Birmingham	4-5pm, PE 227	Statistical Considerations in Clinical Research Studies	Department Invited Speaker Series (STA)
11/10/2016 Thursday	Charles Doering	University of Michigan at Ann Arbor	4-5pm, PE 227	Heat Rises: 100 Years of Rayleigh-Bénard Convection
11/17/2016 Thursday	Ken Ono	Emory University	4-5pm, PE 227	Zeta polynomials for modular forms
12/08/2016 Thursday

Abstracts:


Speaker: Phil Harrington
Time/Room: Thursday, 9/22/2016
Title: The Missing Riemann Mapping Theorem in Several Complex Variables

Speaker: Motohico Mulase
Time/Room: Tuesday, 9/27/2016, 4-5pm, PE 227
Title: What awaits us on the other side of the rainbow? A story of quantum curves and opers
Abstract: Mathematicians keep their childhood dream for a long time. You might have wondered what awaited you if you went over the rainbow. Is the world on the other side of the rainbow the same as what we know? Sir George Biddel Airy discovered the rainbow integral and explained the classical analysis of rainbows. 150 years later, Kontsevich found that the same formula determined the multiplication table of cohomology classes on the compactified moduli spaces of Riemann surfaces. These stories are a simple example of a new mathematical theory of "quantum curves." A general framework of quantum curves will be presented. The talk is based on my joint work with Dr. Dumitrescu.

Speaker: Carl Cowen
Time/Room: Thursday, 10/20/2016, 4-5pm, PE227
Title: Thoughts on Invariant Subspaces for Operators on Hilbert Spaces
Abstract: The Invariant Subspace Question, that is, deciding whether linear operators on Banach or Hilbert spaces have non-trivial invariant subspaces, has been around nearly since the beginning of functional analysis. If $T$ is an operator on a Banach or Hilbert space, a subspace $M$ is said to be invariant for $T$ if $x$ in $M$ implies $Tx$ is also in $M$.  Von Neumann had proved that compact operators have invariant subspaces earlier than the 1950's, but Enflo and Read showed 30 years ago that there are operators on Banach spaces that have no non-trivial invariant subspaces.  \\[1ex]

\hspace{1em} Rota showed, in 1960, that there are operators $T$ that provide models for every bounded linear operator on a separable, infinite dimensional Hilbert space, in the sense that  given an operator $A$ on such a Hilbert space, there is  $\lambda\neq 0$ and an invariant subspace $M$ for $T$ such that the restriction of $T$ to $M$ is similar to $\lambda A$.  In 1969, Caradus provided a practical condition for identifying such universal operators.   In this talk, we will use the Caradus theorem to exhibit new examples of universal operators and show how they can be used to provide information about invariant subspaces for Hilbert space operators. \\[1ex]  

\hspace{1em} This talk is based on work done over the past five years in collaboration with Eva~Gallardo-Guti\'errez, Universidad Complutense de Madrid. 



Speaker: Karan Singh
Time/Room: Thursday, 11/03/2016, 4-5 PM, PE227
Title: Statistical Considerations in Clinical Research Studies
Abstract: Investigators conducting research at clinical research centers often ask statisticians, “Does new intervention work? Or can we get something equivalent to the existing one just as effective and more economical?"

Statisticians help clinical researchers design studies, help to choose what data to collect, analyze data from experiments, help interpret the results of the study, and collaborate in writing manuscripts to describe the results. Nearly all clinical research studies involve statistician from beginning to end. Statisticians help researchers make sense of the data collected to decide whether an intervention is working or to find factors that may contribute significantly to outcomes.

In this presentation we present statistical considerations for a research study from beginning to end using practical examples. We hope that it will enhance the understanding of the role a statistician plays in an investigation conducted at a research center.

Speaker: Charles Doering
Time/Room: Thursday, 11/10/2016, 4-5 PM, PE227
Title: Heat Rises: 100 Years of Rayleigh-Bénard Convection
Abstract: Buoyancy forces result from density variations, often due to temperature variations, in the presence of gravity. Buoyancy-driven fluid flows shape the weather, ocean and atmosphere dynamics, the climate, and the structure of the earth and stars. In 1916 Lord Rayleigh published a paper entitled "On Convection Currents in a Horizontal Layer of Fluid, when the Higher Temperature is on the Under Side" introducing the minimal mathematical model of buoyancy-driven fluid flow now known as Rayleigh-Bénard convection.  For a century this model has served as a primary paradigm of nonlinear dynamical systems displaying spontaneous symmetry breaking and pattern formation, chaos and turbulence. Here we describe progress and challenges for the analysis of Rayleigh's model in the strongly nonlinear regime of turbulent convection.

Speaker: Ken Ono
Time/Room: Thursday, 11/17/2016, 4-5pm, PE227
Title: Zeta polynomials for modular forms

Abstract: The speaker will discuss recent work on Manin's theory of zeta polynomials for modular forms. He will describe recent results which confirm Manin's speculation that there is such a theory which arises from periods of newforms. More precisely, for each even weight k>2 newform f, the speaker will describe a canonical polynomial Zf(s) which satisfies a functional equation of the form Zf(s)=Zf(1−s), and also satisfies the Riemann Hypothesis: if Zf(ρ)=0, then Re(ρ)=1/2. This zeta function is arithmetic in nature in that it encodes the moments of the critical values of L(f,s). This work builds on earlier results of many people on period polynomials of modular forms. This is joint work with Seokho Jin, Wenjun Ma, Larry Rolen, Kannan Soundararajan, and Florian Sprung.

Click here for the colloquium schedule in Fall 2015 and Spring 2016.


Click here for the colloquium schedule in Fall 2014 and Spring 2015.