**Seminars and Colloquiums**

for the week of April 25, 2016

for the week of April 25, 2016

*SPEAKER:*

Farbod Shokrieh, Cornell, Monday

Yu-Ting Chen, Harvard, Tuesday

Jerry Bona, UIC, Wednesday

Elise Weir, UTK, Wednesday

Ryan Loga, UTK, Thursday

Clayton Webster, ORNL and UTK, Thursday

*TEA TIME
3:00 pm – 3:30 pm
Monday, Tuesday, & Wednesday
Room: Ayres 401
Hosted By: Kevin and Chris*

**Monday, April 25th **

ALGEBRA SEMINAR

TITLE: Invariants for Jacobians

SPEAKER: Farbod Shokrieh, Cornell

TIME: 3:35pm – 4:25pm

ROOM: Ayres 114

Associated to every smooth curve one can associate a compact group called its Jacobian. Various invariants for Jacobians (such as various (co)homologies, Hodge numbers, number of point over a finite field) are well-studied. A nodal curve maybe thought of as a limit of smooth curves. Its (generalized) Jacobian is usually not compact. However, they have various nice compactifications depending on some combinatorial data (arising from the way that irreducible components meet each other). I will describe how one can compute some very general invariants for these objects. The solution relies on some subtle combinatorial techniques. This talk is based on joint work with Alberto Bellardini.

** Tuesday, April 26th **

STOCHASTICS SEMINAR

TITLE: Non-uniqueness in SPDEs with non-Lipschitz noise coefficients

SPEAKER: Yu-Ting Chen, Harvard

TIME: 2:10pm – 3:25pm

ROOM: Ayres 114

** Wednesday, April 27th **

COMPUTATIONAL AND APPLIED MATHEMATICS (CAM) SEMINAR

TITLE: Some dynamical problems arising in blood flow

SPEAKER: Jerry Bona, UIC

TIME: 3:35pm – 4:35pm

ROOM: Ayres 113

Pulmonary arterial hypertension is an insidious disease that currently has poor prospects for treatment. In an effort to better understand this disease, a model is developed for blood flow in the relevant part of the body. The model is shown to have at least some predictive capability. A plan is then outlined for using the model in conjunction with laboratory data to begin fathoming the remodeling that is a hallmark of the condition, and which is oftentimes the cause of premature death.

ORAL SPECIALTY EXAM

SPEAKER: Elise Weir, UTK

TIME: 3:35pm – 4:35pm

ROOM: Ayres 114

Her committee consist of Professors: Thistlethwaite (Chair), Conant, and Jameson.

** Thursday, April 28th **

DOCTORAL DEFENSE

SPEAKER: Ryan Loga, UTK

TIME: 11:00am – 12:00pm

ROOM: Ayres 405

His committee consist of Professors: Frazier (Chair), Lind, Phan, Richter, and Guidry (Physics)

SPECIAL COLLOQUIUM

TITLE: Best s-term polynomial approximations of high-dimensional parameterized partial differential equations.

SPEAKER: Clayton Webster, ORNL and UTK

TIME: 3:40pm - 4:35pm

ROOM: Ayres 405

In this talk, we present a new generalized methodology for constructing and analyzing best s-term polynomial approximations, applicable to a wide class of parameterized PDEs with both deterministic and stochastic inputs. Such methods construct a quasi-optimal multi-index set that corresponds to the best s-terms, based on sharp estimates of the polynomial coefficients. Our approach for analyzing the asymptotic truncation error avoids the use of the standard Stechkin inequality, but is instead based on an extension of the underlying multi-index set into a continuous domain, and then an approximation of the cardinality (number of integer multi-indices) by its Lebesgue measure. We consider several cases of d-dimensional affine and non-affine input data, and our proofs reveal sharp asymptotic error estimates in which we achieve sub-exponential convergence rates with respect to the total number of degrees of freedom. In addition, we are also interested in high-dimensional solutions that are characterized by a rapidly decaying polynomial expansion, whose most important terms are captured by a lower (or downward closed) set. By exploiting this fact, we also developed innovative compressed sensing techniques which impose the lower set structure, leading to a provably reduced sample complexity. Using these approaches, the best s-term recovery is established through an improved bound for restricted isometry property for general bounded orthonormal systems. Computational evidence complements our theory and shows the advantage of our generalized methodologies compared to existing approaches and current published results.

**Friday, April 29th **

NO COLLOQUIUM

*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