Seminars and Colloquiums
for the week of April 13, 2009
Speakers:
Mr. Marco Martinez, Monday
Assistant Professor Steve Wise, Monday
Mr. Shiying Si, Tuesday
Assistant Professor Remus Nicoara, Wednesday
Ms. Anastasiia Tsvietkova , Thursday
Professor Bin Xie, Shinshu University, Japan, Thursday
Dr. Jeffrey Paul Wheeler, University of Pittsburgh, Thursday
Dr. Colin Adams, Williams College, Friday
Monday, April 13
MATH ECOLOGY SEMINAR
TIME: 11:15-12:05
ROOM: Dabney 575
SPEAKER: Marco Martinez
TITLE: “Tumor Modeling”
DE/APPLIED MATH & COMPUTATIONAL SCIENCE SEMINAR
TIME: 3:35-4:35 p.m.
ROOM: HBB 102
SPEAKER: Assistant Professor Steve Wise
TITLE: “Energy Stable and Convergent Schemes for the Phase Field Crystal (PFC)and Modified Phase Field Crystal (MPFC) Equations”
ABSTRACT: The PFC and MPFC equations model crystals at the atomic scale in space but on diffusive scales in time. These are sixth-order nonlinear PDEs of parabolic and hyperbolic type, respectively. The models accounts for the periodic structure of a crystal lattice through a free energy functional of Swift-Hohenberg type that is minimized by periodic functions. They naturally incorporate elastic and plastic deformations, multiple crystal orientations and defects and have already been used to simulate a wide variety of crystalline microstructures. In this talk I describe energy stable and convergent finite difference schemes and their efficient solution using a nonlinear multigrid method. A key point in the numerical analysis is the convex splitting of the functional energy corresponding to the gradient systems. In more detail, the physical energy in both cases can be decomposed into purely convex and concave parts. The convex part is treated implicitly, and the concave part is updated explicitly in the numerical schemes. The proposed schemes are unconditionally stable in terms of their respective energies and unconditionally solvable, properties which allow for arbitrarily large time step sizes. This last aspect is vital for coarsening studies that require very large time scales.
Tuesday, April 14
DOCTORAL DEFENSE
TIME: 9:00 a.m.
ROOM: AC 113
SPEAKER: Mr. Shiying Si
TITLE: "Two-step variations for processes driven by fractional Brownian motion with application in testing for jumps from the high frequency data"
His committee consists of Professors: Rosinski (chair), Chen, Xiong, and Daves (Finance).
Wednesday, April 15
WORKSHOP ON COARSE GEOMETRY
TIME: 4:35 – 5:25 p.m.
ROOM: AC 113
SPEAKER: Assistant Professor Remus Nicoara
TITLE: “Introduction to Kazhdan's property (T) III”
ABSTRACT: We give an introduction to property (T) for groups. We present several equivalent definitions, give examples and discuss connections to amenability. Property (T) is a rigidity property introduced by Kazhdan in 1967, which turned out to play an important role in various subjects, including ergodic theory, Lie groups, operator algebras, coarse geometry and graph theory. Graduate students are encouraged to attend.
Thursday, April 16
ORAL SPECIAL EXAMINATION
TIME: 8:00 a.m.
ROOM: JHB 413
SPEAKER: Ms. Anastasiia Tsvietkova
Her committee consists of Professors: Thishlethwaite (chair), Plaut, and Conant.
PROBABILITY SEMINAR
TIME: 12:40 p.m.
ROOM: HBB 132
SPEAKER: Professor Bin Xie, Shinshu University, Japan
TITLE: “A singular SPDE and its invariant measures”
ABSTRACT: We are aiming to present a new
attempt for the stochastic partial differential equations in
relation to the invariant measures. We show that
the distributions of Levy processes are the only invariant
measures of a stochastic heat equation driven by a singular noise,
under a mild technique restriction on Levy measures.
COLLOQUIUM
TIME: 2:30 – 3:30 p.m.
ROOM: AC 113A
SPEAKER: Dr. Jeffrey Paul Wheeler, University of Pittsburgh
TITLE: "The Cauchy-Davenport Theorem and the Erd\H{o}s-Heilbronn Problem for Finite Groups"
ABSTRACT: "Additive Combinatorics can be succinctly stated to be the study of additive structures in sets. The subject has drawn the attention of such minds as Terence Tao, Van Vu, Ben Green, Imre Ruzsa, and others. Part of the attraction to Additive Combinatorics is its connection to other areas of Mathematics such as Number Theory, Ergodic Theory, Graph Theory, Finite Geometry, and even Group Theory. In this talk, we will explore the connection with Group Theory as we consider two classic results.
In particular, we will look at the Cauchy-Davenport Theorem which states that for any two nonempty subsets $A$ and $B$ of $\mathbb{Z}/p\mathbb{Z}$ we have $|A+B| \geq \min \{ p, |A|+|B|-1 \}$ where $A+B$ is the set of sums $a+b \mod p$ with $a \in A$ and $b \in B$. As well we consider the Erd\H{o}s-Heilbronn Problem, proven for the case $A=B$ in $1994$ by Dias da Silva and Hamidoune and the $A \neq B$ case in $1995$ by Alon, Nathanson, and Ruzsa (using the Polynomial Method), which states that for any two nonempty subsets $A$ and $B$ of $\mathbb{Z}/p\mathbb{Z}$ we have $|A \dot{+} B| \geq \min \{ p, |A|+|B|-3 \}$, where $A \dot{+} B$ is the set of sums $a+b \mod p$ with $a \in A$, $b \in B$ and $a \neq b$. We generalize these results from $\mathbb{Z}/p\mathbb{Z}$ to arbitrary finite (including non-abelian) groups.
The beginning of the talk will be accessible to anyone that understands modular arithmetic. The audience will be reminded of the necessary definitions from Group Theory and though theorems will be stated, the proofs will only be briefly discussed."
--Refreshments in AC 113A at 2:10 p.m.
Friday, March 17
COLLOQUIUM
TIME: 3:35 – 4:25 p.m.
ROOM: HBB 102
SPEAKER: Dr. Colin Adams, Williams College
TITLE: “Three Knotty Tales: Complementary Regions, Spiral Index and Spanning Surfaces”
ABSTRACT: In this talk, we will consider three questions related to projections of knots. 1. If we restrict the complementary regions of knot projections, say for instance allowing only triangles, quadrilaterals and pentagons, what knots can we create? 2. If we draw knot projections without any inflection points, so they always curve the same direction, are we just getting versions of braids? 3. Given a single alternating projection of a knot, what can we say about the collection of all spanning surfaces for the knot? All three questions have somewhat surprising answers. No particular background assumed for this talk.
--Refreshments in AC 113 at 3:15 p.m.
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 Dr. Steve Wise.
Week of:
3/16/09 (spring break)
Past notices:
Seminars from 2007-2008 academic year
Seminars from 2006-2007 academic year