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Eberly College of Science Mathematics Department

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<>November 2014
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November 2014
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November 3rd, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Aerodynamic Design Optimization by A Continuous Adjoint Method
Speaker: Feng Liu, University of California, Irvine (Host: J Xu)
Location: MB114
Abstract: http://fliu.eng.uci.edu

I will present our latest research progress on the development of a continuous adjoint method to perform aerodynamic design optimization of wings and turbomachinery blade rows. This method requires only about twice the computational effort of flow calculation to obtain the complete gradient information at each operating condition, regardless of the number of design parameters. Therefore, it is orders-of-magnitude more efficient than a conventional finite-difference method for obtaining the gradient information in a optimization procedure when the design parameters are in the hundreds and more. Examples of single and multiple-point design of transonic wings and turbomachinery blade rows will be presented.

November 3rd, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Multiple Numerical Solutions and Stability of Transonic Flows over Airfoils
Speaker: Feng Liu, University of California, Irvine (Host: J Xu)
Location: MB106
Abstract: http://fliu.eng.uci.edu

Following a general presentation on the numerical simulation of steady and unsteady transonic flows over wings and turbomachinery blade rows by using computational fluid dynamics, I will focus on the findings of multiple numerical solutions for the Transonic Small-Disturbance equation and the Euler equations. Both symmetric and asymmetric solutions are possible for a symmetric airfoil at zero angle of attack within a certain free-stream Mach number range. The stability of the multiple solutions is analyzed using numerical methods. It is found, the symmetric solutions tend to be unstable, while the asymmetric solutions are stable. I will discuss the relevance of such stability analysis to the intrinsic unsteady behavior of transonic buffet over airfoils and wings.

November 3rd, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Krieger's finite generator theorem for ergodic actions of countable groups
Speaker: Brandon Seward, University of Michigan
Location: MB114

The classical Krieger finite generator theorem states that if a free ergodic probability-measure-preserving action of Z has entropy less than log(k), then the action admits a generating partition consisting of k sets. This was extended to actions of amenable groups independently by Rosenthal and Danilenko-Park. We introduce the notion of Rokhlin entropy which is defined for actions of arbitrary countable groups. In the case of actions of amenable groups, Rokhlin entropy coincides with classical entropy and can thus be viewed as a natural extension of classical entropy. Using this notion of entropy, we prove Krieger's finite generator theorem for actions of arbitrary countable groups.

November 4th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: The compactness theorem for continuous model theory
Speaker: Jake Pardo, Penn State
Location: MB315

The talk will present a proof of the compactness theorem for continuous logic, using ultraproducts of metric spaces.

November 4th, 2014 (02:30pm - 03:30pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Cocycle Reduction and Exponential Drift
Speaker: Alex Eskin, University of Chicago
Location: MB114

I will be discussing how some cocycle reduction results can be combined with the exponential drift technique of Benoist-Quint to prove some measure rigidity results, in particular for the SL(2,R) action on moduli space. This is joint work with Maryam Mirzakhani. Note: this talk will be self-contained, and no knowledge of Teichmuller theory will be assumed (or needed).

November 4th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Pointwise convergence of multiple ergodic averages and strictly ergodic models
Speaker: Xiangdong Ye, University of Science and Technology of China
Location: MB216

In this talk we discuss the pointwise convergence. By building some suitable strictly ergodic models, we prove that for an ergodic system $(X,\mathcal{X},\mu, T)$, $d\in\N$, $f_1, \ldots, f_d \in L^{\infty}(\mu)$, the averages $$\frac{1}{N^2} \sum_{(n,m)\in [0,N-1]^2} f_1(T^nx)f_2(T^{n+m}x)\ldots f_d(T^{n+(d-1)m}x)$$ converge $\mu$ a.e. Deriving some results from the construction, for distal systems we answer positively the question if the multiple ergodic averages converge a.e. That is, we show that if $(X,\mathcal{X},\mu, T)$ is an ergodic distal system, and $f_1, \ldots, f_d \in L^{\infty}(\mu)$, then the multiple ergodic averages $$\frac 1 N\sum_{n=0}^{N-1}f_1(T^nx)\ldots f_d(T^{dn}x)$$ converge $\mu$ a.e.. The two talks are mainly based on the following papers. a. S. Shao and X.Ye, Regionally proximal relation of order d is an equivalence one for minimal systems and a combinatorial consequence,Adv. in Math.,231(2012), 1786-1817. b. W. Huang, S. Shao and X. Ye,Nil Bohr-sets and almost automorphy of higher order, arXiv:1407.1179v1[math.DS], Memoirs of Amer. Math. Soc., to appear. c. W. Huang, S. Shao and X Ye, Pointwise convergence of multiple ergodic averages and strictly ergodic models, arXiv:1406.5930v1[math.DS], submitted.

November 4th, 2014 (04:00pm - 05:00pm)
Seminar: Applied Analysis Seminar
Title: Extremality, uniqueness and optimality of transference plans.
Speaker: Stefano Bianchini, SISSA, Italy
Location: MB106

For the transportation problem \[ \inf \int c(x,y) \pi \] where $\pi$ (the transference plan) is a probability measure with given marginals, and $c$ is a Borel cost, we are interested in the characterization of the minimizers (optimal plans). Analogous problems are the characterization of extremal points of the set of transference plans and its uniqueness. Even if the result is measure theoretic, it has applications to the solution of the Monge problem (existence of an optimal map) for convex l.s.c. costs.

November 5th, 2014 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: Some results on the compressible Navier-Stokes equations with density-dependendt viscosity (part II)
Speaker: Mingjie Li, Minzu University of China
Location: MB106

We talk about some a priori estimations on the 1D compressible Navier-Stokes equations with density-dependendt viscosity which based on the special structure of equations. From these estimations we can study the behavior of vacuum state and blow up phenomena of the flow. Then we extend these a priori estimations into Multi-Dimensional case.

November 5th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Proficiency to Mastery (Week 1 of 3)
Speaker: Attendees, Penn State
Location: MB102

For the next three weeks, we discuss what it means for a student to be proficient and to develop mastery. We will be reading excerpts from Adding it Up and How Learning Works. This week, we read the description of proficiency from Adding It Up.
Kilpatrick, Jeremy, Jane Swafford, and Bradford Findell. "The Strands of Mathematical Proficiency." Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy, 2001. 115-35. Print.

November 6th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Portraits of rational functions modulo primes
Speaker: Tom Tucker, University of Rochester
Location: MB106

Let F be a rational function of degree > 1 over a number field or function field K and let z be a point that is not preperiodic. Ingram and Silverman conjecture that for all but finitely many positive integers (m,n), there is a prime p such that z has exact preperiodic m and exact period n (we call this pair (m,n) the portrait of z modulo p). We present some counterexamples to this conjecture and show that a generalized form of abc implies -- one that is true for function fields -- implies that these are the only counterexamples. One may also ask a similar question for tuples of portraits for several point in a number field or function field. This work is still in progress. The talk represents joint work with several other authors.

November 6th, 2014 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Solutions to polynomials in two variables
Speaker: Thomas Tucker, University of Rochester
Location: MB114

You may remember the quadratic formula for finding solutions to quadratic polynomials in one variable. It is natural to ask: are there formulas like this for polynomials of higher degree? The answer, roughly speaking, is yes. Going further, one might ask: what about polynomials in more than one variable? Here, the answer is far more complicated, and involves geometry in what may seem a surprising way. One famous example of this type of polynomial equation is the Fermat equation x^n + y^n = z^n.

November 7th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Limit distribution of return times to shrinking targets
Speaker: Xuan Zhang, PSU
Location: MB106

We revisit the problem of finding limit exponential laws for return times to shrinking targets and study a more general problem of finding limit distribution for stopping times when partial sums of bounded positive functions exceed a threshold. We give a sufficient condition for the limit distribution of these stopping times to exist and discuss some examples.

November 10th, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Orbits closures for the action of SL(2,R) on moduli spaces.
Speaker: Amir Mohammadi, University of Texas, Austin
Location: MB114

There is an action of SL(2,R) on the moduli space of a compact Riemann surface which is expected to have similar rigidity properties as in the theory of unipotent flows on homogeneous spaces. In this talk we will discuss a joint work with Eskin and Mirzakhani in which orbits closures of this action are studied. The main ingredients are a measure rigidity theorem of Eskin and Mirzakhani, and a certain avoidance principle which we develop using ideas of Margulis.

November 11th, 2014 (01:00pm - 01:50pm)
Seminar: Mathematical Biology Colloquium
Title: Cell motility as a free boundary problem
Speaker: Alex Mogilner, Courant Institute, NYU
(Host: Leonid Berlyand)
Location: MB106

Cells migrate on surfaces by protruding their front through growth of actin networks, retracting the rear by myosin-driven contraction and adhering to the substrate. Recent experimental and modeling efforts elucidated molecular and mechanical processes that allow motile cells to maintain steady shape and speed. These processes are multiple and redundant, and the challenge is to understand how molecular machines operating on multiple scales synergize to initiate motility and allow the cell to move steadily or to turn. Mathematically and mechanically, the cell is a contractile and viscous actomyosin gel with free boundary. I will describe modeling of the simplest motile cell, fish keratocyte, and discuss future challenges in simulating more complex cells.

November 11th, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Integration of singular foliations and usage
Speaker: Iakovos Androulidakis, University of Athens
Location: MB106

We discuss two aspects of integration, one in the (classical) spirit of Sophus Lie and the other in the framework of operator algebras. Starting from the context of regular foliations, we explain the evolution of these processes first to the almost regular case by C. Debord, and finally to singular foliations in full generality (joint work with G. Skandalis). We also give the use of these integration processes; the first integration provides a normal form of the foliation around a (singular) leaf, and the second leads to calculations of the spectrum for longitudinal Laplace operators.

November 12th, 2014 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: PDE models for Ferrofluids and their Numerical Analysis
Speaker: Ignacio Tomas, University of Maryland
Location: MB106

A ferrofluid is a liquid which becomes strongly magnetized in the presence of applied magnetic fields. In this talk we will survey some models for ferrofluids: their physical origins, PDE models, and related numerics. There are two generally accepted ferrofluid models which we will call by the name of their developers: the Rosensweig and Shliomis model. We will start by developing a numerical scheme for the Rosensweig model and carefully track the requirements to devise of an energy-stable scheme. Both the Rosensweig and Shliomis models deal with one-phase flows, which is the case of many technological applications. However, many applications arise naturally in the form of a two-phase flow: one of the phases has magnetic properties and the other one does not (e.g. magnetic manipulation of microchannel flows, microvalves, magnetically guided transport, etc). We have also developed a matching-density two-phase ferrofluid model starting from the simplified framework of the Shliomis model and the Cahn-Hilliard equation. This model satisfies an energy law, and with the lessons learned from the Rosensweig model, we were able to devise an energy-stable scheme. In addition, with some simplifications of the two-phase model, it is possible to prove convergence of the scheme, and as a by product, existence of solutions of the simplified PDE system. Finally, I will illustrate the capabilities of the numerical schemes with some numerical simulations.

November 12th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Proficiency to Mastery (Week 2 of 3)
Speaker: Attendees, Penn State
Location: MB102

For the next three weeks, we discuss what it means for a student to be proficient and to develop mastery. We will be reading excerpts from Adding it Up and How Learning Works. This week, we consider if students are proficient based on results summarized in Adding It Up.
Kilpatrick, Jeremy, Jane Swafford, and Bradford Findell. "The Strands of Mathematical Proficiency." Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy, 2001. 136-55. Print.

November 13th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: To be announced
Speaker: Sevak Mkrtchyan, University of Rochester
Location: MB106
November 13th, 2014 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: TBA
Speaker: Richard Schwartz, Brown University
Location: MB114
November 14th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: TBA
Speaker: Xiaofeng Zheng, PSU
Location: MB106
November 17th, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: TBA
Speaker: Rodrigo Treviño, Cornell University
Location: MB114
November 18th, 2014 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Results on simultaneous core partitions
Speaker: Dr. Rishi Nath, York College, CUNY
Location: MB106

Simultaneous core partitions were first investigated in 1999 by J. Anderson. A recent conjecture by D. Armstrong on the average size of a simultaneous (s,t)-core; and subsequent work by R. Stanley and F. Zanello on the (s, s+1) (Catalan) case has renewed interest in this area. We will survey the main results in the field--highlighting connections with posets, actions of the affine symmetric group, and the GBG-rank--and offer new results on simultaneous (s, s+2)-cores.

November 18th, 2014 (01:00pm - 01:50pm)
Seminar: Theoretical Biology Seminar
Title: TBA
Speaker: Rafael Meza, University of Michigan
(Host: Jessica Conway)
Location: MB106
November 18th, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: The symplectic displacement energy
Speaker: Augustin Banyaga, Penn State
Location: MB106

We show that the symplectic displacement energy of a non-empty open subset of a compact symplectic manifold (i.e. the infimum of the Hofer-like norms of symplectic diffeomorphisms that displace the subset) is a strictly positive number. We apply this fact to prove a result that justifies the introduction of the notion of strong symplectic homeomorphisms. This is a joint work with David Hurtubise and Peter Spaeth.

November 18th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Dynamics near low-dimensional attractors of neural networks.
Speaker: Vladimir Itskov, Penn State
Location: MB216

After a brief introduction to generic rate models of neural networks I will talk about "continuous attractor networks" that are hypothesized to underlie some critical functions in the mammalian brain. These networks are perturbations of systems that have a low-dimensional submanifold of steady states in the continuum limit. I will discuss basic properties of such networks and also pose some open questions.

November 18th, 2014 (03:35pm - 04:25pm)
Seminar: Center for Interdisciplinary Mathematics Seminar
Title: Motility at microscopic scales
Speaker: Antonio De Simone, International School for Advanced Studies, Trieste, Italy
Location: MB114
Abstract: http://

Motility of cells is at the root of many fundamental processes in biology: from sperm cells swimming to fertilize an egg cell, to leukocytes migrating towards newly opened wounds to activate the response of the immune, to metastatic tumor cells crawling to invade nearby tissues. We will discuss the mechanical bases of cellular motility by swimming and crawling. Special emphasis will be placed on the connections between low Reynolds number swimming and Geometric Control Theory, and on the geometric structure of the underlying equations of motion. We will then examine some concrete example, taken from the case studies that have been recently considered by our group and including: reverse engineering of the euglenoid movement, undulatory locomotion of snake-like robots, and one-dimensional models of slender crawlers. Finally, we will re-examine the lessons learned in the context of biological cell motility with the aim of building a dictionary of elementary motility mechanism to be used in prototypes of bio-inspired motile micro-robots.

November 19th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Proficiency to Mastery (Week 3 of 3)
Speaker: Attendees, Penn State
Location: MB102

For the next three weeks, we discuss what it means for a student to be proficient and to develop mastery. We will be reading excerpts from Adding it Up and How Learning Works. This week, we read about Mastery from How Learning Works.
Ambrose, Susan A. "How Do Students Develop Mastery." How Learning Works: Seven Research-based Principles for Smart Teaching. San Francisco, CA: Jossey-Bass, 2010. 91-120. Print.

November 20th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Zagier polynomials and modified N\"{o}rlund polynomials
Speaker: Atul Dixit
Location: MB106

In 1998, Don Zagier studied the numbers B_{n}^{*} which he called the 'modified Bernoulli numbers'. They satisfy amusing variants of the properties of the ordinary Bernoulli numbers. Recently, Victor H. Moll, Christophe Vignat and I studied an obvious generalization of the modified Bernoulli numbers, which we call 'Zagier polynomials'. These polynomials are also rich in structure, and we have shown that a theory parallel to that of ordinary Bernoulli polynomials exists. Zagier showed that his asymptotic formula for B_{2n}^{*} can be replaced by an exact formula. In an ongoing joint work with M. L. Glasser and K. Mahlburg, we have shown that a similar thing is true for the Zagier polynomials. This exact formula involves Chebyshev polynomials and infinite series of Bessel function $Y_{n}(z)$. Through a motivation coming from diffraction theory, C. M. Linton has already proved this, but in a disguised form, and our proof is new and gives new results along the way. We also derive Zagier's formula as a limiting case of this general formula, which is interesting in itself. In the second part of my talk, I will discuss another generalization of the modified Bernoulli numbers that we recently studied along with A. Kabza, namely 'modified N\"{o}rlund polynomials' B_{n}^{(\alpha)*}, \alpha\in\mathbb{N}, and obtain their generating function along with applications.​ The talk will include an interesting mix of special functions, number theory, probability and umbral calculus.

November 21st, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: TBA
Speaker: Weining Kang, University of Maryland
Location: MB106
November 24th, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Fall Break, No Seminar
Speaker: Fall Break, No Seminar
Location: MB114
November 24th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Fall Break, No Seminar
Speaker: Fall Break, No Seminar
Location: MB106
November 27th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: No meeting
Speaker: Mr Turkey, Thanksgiving
Location: MB106
November 27th, 2014 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Thanksgiving Break
Speaker: Thanksgiving Break
Location: MB114