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Today, Tuesday, January 23, 2018

Algebra and Number Theory Seminar  Questions or comments?

Posted November 30, 2017
Last modified January 22, 2018

3:10 pm - 4:00 pm 285 Lockett

William Casper, Louisiana State University
Algebras of Differential Operators and Algebraic Geometry with Applications


Computational Mathematics Seminar  

Posted January 16, 2018

3:30 pm - 4:30 pm 1034 Digital Media Center

Amanda Diegel, Louisiana State University
The Cahn-Hilliard Equation, a Robust Solver, and a Phase Field Model for Liquid Crystal Droplets

Abstract: We begin with an introduction to the Cahn-Hilliard equation and some motivations for the use of phase field models. We will then go on to describe a first order finite element method for the Cahn-Hilliard equation and the development of a robust solver for that method. The key ingredient of the solver is a preconditioned minimal residual algorithm (with a multigrid preconditioner) whose performance is independent of the spatial mesh size and the time step size for a given interfacial width parameter. In the second part of the talk, we present a novel finite element method for a phase field model of nematic liquid crystal droplets. The model considers a free energy comprised of three components: the Ericksen''s energy for liquid crystals, the Cahn-Hilliard energy for phase separation, and an anisotropic weak anchoring energy that enforces a boundary condition along the interface between the droplet and surrounding substance. We present the key properties of the finite element method for this model including energy stability and convergence and conclude with a few numerical experiments.

Tomorrow, Wednesday, January 24, 2018

Colloquium  Questions or comments?

Posted January 12, 2018
Last modified January 17, 2018

3:30 pm - 4:20 pm Lockett 241

Christine Lee, University of Texas at Austin
Understanding quantum link invariants via surfaces in 3-manifolds

Abstract: Quantum link invariants lie at the intersection of hyperbolic geometry, 3-dimensional manifolds, quantum physics, and representation theory, where a central goal is to understand its connection to other invariants of links and 3-manifolds. In this talk, we will introduce the colored Jones polynomial, an important example of quantum link invariants. We will discuss how studying properly embedded surfaces in a 3-manifold provides insight into the topological and geometric content of the polynomial. In particular, we will describe how relating the definition of the polynomial to surfaces in the complement of a link shows that it determines boundary slopes and bounds the hyperbolic volume of many links, and we will explore the implication of this approach on these classical invariants.

Friday, January 26, 2018

Colloquium  Questions or comments?

Posted January 19, 2018
Last modified January 21, 2018

3:30 pm - 4:20 pm Lockett 241

Shawn X. Cui, Stanford, Institute for Theoretical Physics
Four Dimensional Topological Quantum Field Theories

Abstract: We give an introduction to topological quantum field theories (TQFTs), which have wide applications in low dimensional topology, representation theory, and topological quantum computing. In particular, TQFTs provide invariants of smooth manifolds. We give an explicit construction of a family of four dimensional TQFTs. The input to the construction is a class of tensor categories called $G$-crossed braided fusion categories where $G$ is any finite group. We show that our TQFTs generalize most known examples such as Yetter's TQFT and the Crane-Yetter TQFT. It remains to check if the resulting invariant of 4-manifolds is sensitive to smooth structures. It is expected that the most general four dimensional TQFTs should arise from spherical fusion 2-categories, the proper definition of which has not been universally agreed upon. Indeed, we prove that a $G$-crossed braided fusion category corresponds to a 2-category which does not satisfy the criteria to be a spherical fusion 2-category as defined by Mackaay. Thus the question of what axioms properly define a spherical fusion 2-category is open.

Tuesday, January 30, 2018

Algebra and Number Theory Seminar  Questions or comments?

Posted November 30, 2017

3:10 pm - 4:00 pm

William Casper, Louisiana State University
TBA

Wednesday, January 31, 2018

Colloquium  Questions or comments?

Posted January 22, 2018

3:30 pm - 4:20 pm Lockett 241

Larry Rolen, Trinity College Dublin & Georgia Tech
tba

Friday, February 2, 2018

Colloquium  Questions or comments?

Posted January 21, 2018

3:30 pm - 4:20 pm Lockett 241

Chun-Hung Liu, Princeton University
tba

Monday, February 5, 2018

Applied Analysis Seminar  Questions or comments?

Posted January 10, 2018

3:30 pm - 4:30 pm Lockett 233

Prashant Kumar Jha, LSU
TBA

Tuesday, February 20, 2018

Algebra and Number Theory Seminar  Questions or comments?

Posted November 30, 2017
Last modified January 16, 2018

3:10 pm - 4:00 pm

Peng-Jie Wong, University of Lethbridge
Holomorphy of L-functions and distribution of primes

The analytic properties of L-functions have been one of the central topics in number theory as they have many arithmetic applications. For example, the distribution of prime numbers has a deep connection with the properties of the Riemann zeta function. In general, for any number field, there are primes and L-functions of similar nature. In this talk, we shall discuss the holomorphy of such L-functions and its applications to the distributions of the associated primes.

Monday, February 26, 2018

Applied Analysis Seminar  Questions or comments?

Posted January 11, 2018

3:30 pm - 4:30 pm Lockett 233

Wei Li, LSU
TBA

Wednesday, February 28, 2018

Topology Seminar  Seminar website

Posted November 13, 2017

3:30 pm - 4:30 pm Lockett 233

Ivan Levcovitz, CUNY Graduate Center
TBD

Monday, March 5, 2018

Applied Analysis Seminar  Questions or comments?

Posted January 10, 2018

3:30 pm - 4:30 pm Lockett 233

Masato Kimura, Kanazawa University, Japan
TBA

Tuesday, March 6, 2018

Algebra and Number Theory Seminar  Questions or comments?

Posted January 15, 2018

3:10 pm - 4:00 pm

Wen-Ching Winnie Li, Pennsylvania State University
TBA

Wednesday, March 7, 2018

Topology Seminar  Seminar website

Posted October 18, 2017

3:30 pm - 4:30 pm Lockett 233

Bulent Tosun, University of Alabama
TBD

Thursday, March 8, 2018

Colloquium  Questions or comments?

Posted December 17, 2017

3:30 pm - 4:20 pm TBD

Habib Ouerdiane, University of Tunis El Manar
TBD

Monday, March 12, 2018

Applied Analysis Seminar  Questions or comments?

Posted January 16, 2018

3:30 pm - 4:30 pm Lockett 233

Tadele Mengesha, The University of Tennessee, Knoxville
TBA

Wednesday, March 14, 2018

Topology Seminar  Seminar website

Posted October 18, 2017

3:30 pm - 4:30 pm

Ina Petkova, Dartmouth College
TBD

Tuesday, March 20, 2018

Algebra and Number Theory Seminar  Questions or comments?

Posted January 16, 2018

3:10 pm - 4:00 pm

Rina Anno, Kansas State University
TBA

Wednesday, March 21, 2018

Topology Seminar  Seminar website

Posted January 10, 2018
Last modified January 12, 2018

3:30 pm - 4:30 pm Lockett 233

Adam Levine, Duke University
TBD

Thursday, March 22, 2018

Colloquium  Questions or comments?

Posted December 17, 2017

3:30 pm - 4:20 pm TBD

Guozhen Lu, University of Connecticut
TBD

Wednesday, April 4, 2018

Pasquale Porcelli Lecture Series  Special Lecture Series

Posted November 7, 2017
Last modified January 4, 2018

2:30 pm - 3:30 pm tba

Irene Fonseca, Carnegie Mellon University
Porcelli Lecture 1: The Mathematics of Inpainting

(The talk is intended to be accessible to High School Students.) In this talk we will illustrate how mathematical techniques can be used in image processing. These play an important role in the creation of digital inpainting methods with a wide spectrum of applications, such as in the process of image restoration of ancient frescoes where missing parts of damaged images are filled in based on the information collected from neighboring areas.


Pasquale Porcelli Lecture Series  Special Lecture Series

Posted November 7, 2017
Last modified January 4, 2018

4:10 pm - 5:10 pm tba

Irene Fonseca, Carnegie Mellon University
Porcelli Lecture 2: Variational Problems in Materials Science

(Intended to be accessible to Undergraduate Students.) Abstract: Quantum dots are man-made nanocrystals of semiconducting materials. Their formation and assembly patterns play a central role in nanotechnology, and in particular in the optoelectronic properties of semiconductors. Changing the dots' size and shape gives rise to many applications that permeate our daily lives, such as the new Samsung QLED TV monitor that uses quantum dots to turn "light into perfect color"! Quantum dots are obtained via the deposition of a crystalline overlayer (epitaxial film) on a crystalline substrate. When the thickness of the film reaches a critical value, the profile of the film becomes corrugated and islands (quantum dots) form. As the creation of quantum dots evolves with time, materials defects appear. Their modeling is of great interest in materials science since material properties, including rigidity and conductivity, can be strongly influenced by the presence of defects such as dislocations. In this talk we will use methods from the calculus of variations and partial differential equations to model and mathematically analyze the onset of quantum dots, the regularity and evolution of their shapes, and the nucleation and motion of dislocations.

Thursday, April 5, 2018

Pasquale Porcelli Lecture Series  Special Lecture Series

Posted November 7, 2017
Last modified January 4, 2018

10:30 am - 11:30 am tba

Irene Fonseca, Carnegie Mellon University
Porcelli Lecture 3: Variational Problems in Imaging Science

(The talk is intended to be accessible to Graduate Students.) Abstract: The mathematical treatment of image processing is strongly hinged on variational methods, partial differential equations, and machine learning. The bilevel scheme combines the principles of machine learning to adapt the model to a given data, while variational methods provide model-based approaches which are mathematically rigorous, yield stable solutions and error estimates. The combination of both leads to the study of weighted Ambrosio-Tortorelli and Mumford-Shah variational models for image processing.

Tuesday, April 10, 2018

Algebra and Number Theory Seminar  Questions or comments?

Posted January 15, 2018

3:10 pm - 4:00 pm

Li Guo, Rutgers University at Newark
TBA

Thursday, April 12, 2018

Colloquium  Questions or comments?

Posted December 26, 2017

3:30 pm - 4:20 pm TBD

Stefan Kolb, Newcastle University
TBD

Tuesday, April 17, 2018

Algebra and Number Theory Seminar  Questions or comments?

Posted January 16, 2018

3:10 pm - 4:00 pm

TBA

Thursday, April 19, 2018

Colloquium  Questions or comments?

Posted January 12, 2018

3:30 pm - 4:20 pm TBD

Birge Huisgen-Zimmermann, University of California, Santa Barbara
TBD

Wednesday, April 25, 2018

Topology Seminar  Seminar website

Posted November 12, 2017
Last modified January 8, 2018

3:30 pm - 4:30 pm Lockett 233

Miriam Kuzbary, Rice University
TBD