**Seminars and Colloquiums**

for the week of April 18, 2016

for the week of April 18, 2016

*SPEAKER:*

Vajira Manathunga, UTK, Monday

Morwen Thistlethwaite, UTK, Monday

Elise Weir, UTK, Monday

Thomas Weighill, UTK, Monday

Cheng Wang, Monday

Jan Rosinski, UTK, Tuesday

Urszula Ledzewicz, Tuesday

Ohannes Karakashian, UTK, Wednesday

Monty Taylor, UTK, Thursday

Judy Day, UTK, Thursday

Tomer Lancewicki, UTK Electrical Engineering and Computer Science Dept., Friday

Josh Mike, UTK, Friday

JunCheng Wei, Stanford, Friday

*TEA TIME
3:00 pm – 3:30 pm
Monday, Tuesday, & Wednesday
Room: Ayres 401
Hosted By: Stefan Schnake and Ryan Loga*

**Monday, April 18th **

DOCTORAL DEFENSE

SPEAKER: Vajira Manathunga

TIME: 11:00am – 12:00pm

ROOM: Ayres 114

His committee consists of Professors: Conant (Chair), Brodskiy, Thistlethwaite, and Berry (EECS)

ALGEBRA/ TOPOLOGY SEMINAR

TITLE: Deforming representations of manifold groups

SPEAKER: Morwen Thistlethwaite

TIME: 1:25pm – 2:15pm

ROOM: Ayres 405

We look at representation varieties of fundamental groups of 2- and 3-manifolds into some linear groups.

GEOMETRY AND TOPOLOGY SEMINAR

TITLE: Pseudomodular surfaces

SPEAKER: Elise Weir, UTK

TIME: 2:30pm – 3:20pm

ROOM: Ayres 113

The modular group PSL(2,Z) acts by fractional linear transformations on the upper half plane model of hyperbolic space, which induces a transitive action on ???. We'll start by discussing the geometric picture that arises from this action, including a tessellation of the half plane by hyperbolic triangles. Then we'll dig into a more recent result, due to Long and Reid, that describes examples of subgroups of the modular group which also act transitively on ???. As time permits, we will examine geometric interpretations of the action of these pseudomodular groups, such as an associated tiling of the half plane.

ORAL SPECIALTY EXAM

SPEAKER: Thomas Weighill

TIME: 3:35pm – 4:35pm

ROOM: Ayres 121

His committee consist of Professors: Dydak (chair), Brodskiy, and Thistlethwaite

COMPUTATIONAL AND APPLIED MATHEMATICS (CAM) SEMINAR

TITLE: The Strong-Stability-Preserving (SSP) scheme applied to the Integrating Factor (IF) form of Exponential Time Differencing (ETD) problems

SPEAKER: Cheng Wang

TIME: 3:35pm – 4:35pm

ROOM: Ayres 113

Certain Exponential Time Differencing (ETD) problems are taken into consideration. Since the linear operator exactly preserves the energy norms, we reformulate the ETD problem in the Integrating Factor (IF) form. In turn, the Strong-Stability-Preserving (SSP) schemes could be applied to the reformulated PDE, and a local in time convergence result could be derived via a linearized stability analysis. As a result of this analysis, the third and higher order convergence in time could be theoretically justified, without any condition between the time step and spatial grid sizes. A few examples, including the “Good” Boussinesq equation, nonlinear Schrodinger equation, and nonlinear KDV equation, will be covered.

**Tuesday, April 19th **

STOCHASTICS SEMINAR

TITLE: Isomorphism identities for Poissonian ID processes with applications

SPEAKER: Jan Rosinski, UTK

TIME: 2:10pm – 3:25pm

ROOM: Ayres 114

The classical Cameron-Martin Formula is an isomorphism theorem that expresses a translated Gaussian process (or a random field) in terms of the untranslated process, but with a change of probability measure. Typical applications include SDEs driven by Brownian motion or SPDEs driven by Gaussian random fields. It is well-known, however, that the Cameron-Martin Formula does not extend to a Poisson process. We show that changing deterministic translations to random ones will do the trick, allowing such extensions. We give the framework and the corresponding isomorphism identities for Poissonian ID processes and random fields, and discuss some applications. Coincidentally, the celebrated Dynkin’s isomorphism theorem is a special case of such identities.

NIMBIOS

TITLE: Optimal protocols for combination therapies in cancer: How much, how often, in what sequence?”

SPEAKER: Urszula Ledzewicz

TIME: 3:30pm – 4:30pm

ROOM: Hallam Auditorium, Room 2006, Claxton Education Building

The questions “how much, how often, and in what sequence” anti-cancer drugs should be given to secure an optimal outcome are essential and far from being answered yet. Also, simple answers are not always the best ones. Actually, there is mounting medical evidence that "more is not necessarily better" and a properly calibrated dose that takes into account this complexity can lead to a better outcome. This has generated a search for what is called the biologically optimal dose (BOD) in the medical literature. Formulating mathematical models with an objective that reflects the overall goal of the therapy, like minimizing the tumor size and side effects, maximizing the actions of the immune system, etc., leads to optimal control problems where mathematical analysis can answer some of these questions in a theoretical framework. In this talk, we present some of these problems, addressing challenges and open questions. The results of the analysis will be compared with medical and experimental data.

**Wednesday, April 20th **

COMPUTATIONAL AND APPLIED MATHEMATICS (CAM) SEMINAR

TITLE: TBA

SPEAKER: Ohannes Karakashian, UTK

TIME: 3:35pm – 4:35pm

ROOM: Ayres 113

Abstract: TBA

**Thursday, April 21st **

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: Global Well-Posedness for Schrodinger Equations with Derivative

SPEAKER: Monty Taylor, UTK

TIME: 2:00pm - 3:00pm

ROOM: Ayres 113

JR. COLLOQUIUM

TITLE: Fighting infections with mathematics

SPEAKER: Judy Day, UTK

TIME: 3:40pm - 4:35pm

ROOM: Ayres 405

Chances are you have gotten sick from some kind of infection before, but have thankfully recovered enough to read this abstract! In some cases, unfortunately, infections can be fatal – a reality that clinicians working in intensive care units face every day. What is going on inside when we are sick? In more serious infections, why might recovery not be a possibility? How can we understand this process better so we can properly intervene? We will see how combining mathematics with biology can provide a deeper understanding of the dynamics of an infection and reveal possible strategies for successfully controlling the response.

**Friday, April 22nd **

SIAM STUDENT CHAPTER SEMINAR

TITLE: Options and Futures in financial markets

SPEAKER: Tomer Lancewicki, UTK Electrical Engineering and Computer Science Dept.

TIME: 12:20pm

ROOM: Ayres 405

In the last 40 years, derivatives have become increasingly important in finance and are actively traded on many exchanges throughout the world. Derivatives can be used for hedging, speculation or arbitrage.

They play a key role in transferring a wide range of risks in the economy from one entity to another. Electronic trading has led to a growth in high-frequency and algorithmic trading. This involves the use of computer programs to initiate trades, often without human intervention, and has become an important feature of derivatives markets. In this talk we will explain the key concepts of futures and options. We will examine these concepts on real data sets from an algorithmic trading system.

ANALYSIS SEMINAR

TITLE: Using (quasi-) conformal mappings to define and compute geometric

distances between (disk-type and sphere-type) surfaces.

SPEAKER: Josh Mike, UTK

TIME: 2:30pm – 3:20pm

ROOM: Ayres 121

In talk 2 of 2, we will discuss some applications of conformal and quasiconformal mappings. The theory of conformal mappings can be helpful in describing approximation schema in the geometry of manifolds. For surfaces in particular the notions of conformal and area-preserving diffeomorphism are closely related by the Jacobian and its eigenvalues. A diffeomorphism between surfaces has both properties if and only if that mapping is an isometry. This important relationship lends intuitive meaning to some metrics that we will introduce and discuss. These new metrics will be compared with more traditional metrics such as the Hausdorff distance. This is a recent project/discussion with Brian Allen, so any feedback or suggestions are welcome.

COLLOQUIUM

TITLE: On Tyle II singularity of harmonic map flows

SPEAKER: JunCheng Wei, Stanford

TIME: 3:30pm-4:30pm

ROOM: Ayres 405

*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:**

3/14/2016 - spring break