PSU Mark
Eberly College of Science Mathematics Department

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September 1st, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Labor Day, no classes
Speaker: Labor Day, no classes
Location: MB106
September 2nd, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Systems of conservation laws in one and two space dimensions
Speaker: Yuxi Zheng, Penn State
Location: MB216

We will round up interesting open problems that we will focus on this year.

September 2nd, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Spectral coincidence of transition operators, automata groups and BBS in tropical geometry
Speaker: Tsuyoshi Kato, Kyoto University
Location: MB106

I will speak on our discovery of a spectral coincidence of Markov operators between the lamplighter group and the box-ball system. The former appears in group theory and the latter is the automaton of the KdV equation in in finite integrable systems, passing through tropical geometry. This is joint work with S. Tsujimoto and A. Zuk.

September 2nd, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: An introduction to reverse mathematics
Speaker: Stephen G. Simpson, Penn State
Location: MB315

Reverse mathematics is a program of research in the foundations of mathematics. A basic discovery, emphasized by Hilbert and Bernays in the 1930s, is that the proofs of almost all theorems of core mathematics (analysis, algebra, geometry, combinatorics, ...) are straightforwardly formalizable in subsystems of second-order arithmetic. Reverse mathematics is a series of case studies, initiated in the 1970s, in which specific core mathematical theorems are examined in order to determine the smallest subsystem of second-order arithmetic in which the given theorem is provable. The program of reverse mathematics is very rich, with many sub-programs and many open problems. Many concepts from mathematical logic come into play, including Turing computability, the Turing jump operator, basis theorems, relative hyperarithmeticity, the hyperjump, proof-theoretic ordinals, and nonstandard models of arithmetic. Over the past 40 years, some interesting conclusions have emerged. For instance, it turns out that many core mathematical theorems are logically equivalent to the axioms needed to prove them, and this leads to a robust classification of such theorems up to logical equivalence. Indeed, many such theorems fall into only five equivalence classes, the so-called "Big Five." An area of recent interest is the reverse mathematics of measure theory, which involves algorithmic randomness.

September 2nd, 2014 (02:30pm - 03:30pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Area preserving flows on surfaces: survey and new exceptional behaviour
Speaker: Alex Wright, Stanford University
Location: MB114

Since the 60s, the ergodic behaviour of area preserving flows on surfaces has been extensively studied. We now know that such flows are typically uniquely ergodic and weak mixing, but typically not mixing. In the case of smooth flows on the torus, or straight line flows on translation surfaces, they are never mixing. We will give a brief survey of this story, and explain a new contribution: there exists a mixing smooth flow on a surface with non-degenerate fixed points. Joint work with Jon Chaika.

September 2nd, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: An introduction to the use of algebraic geometry in Teichmuller dynamics, III. ATTENTION: the second lecture in this series will take place on THURSDAY AUGUST 28 3:30-6pm n Teichmuller dynamics,I
Speaker: Alex Wright, Stanford University
Location: MB216
September 3rd, 2014 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: Energetic Derivation of Incompressible Euler and Navier-Stokes systems on an Evolving Hypersurface
Speaker: Hajime Koba, Waseda University
Location: MB106

In this talk, we consider fluid-flow on an evolving hypersurface. We apply our energetic variational approach to study the motion of incompressible inviscid and viscous flow on an evolving hypersurface. More precisely, we derive the incompressible Euler and Navier-Stokes equations on an evolving hypersurface by our energetic variational approach. Our results enable us to understand that the fluid-flow on an evolving hypersurface depend on both the curvature and the speed of an evolving hypersurface. This research relates to two phase flow problems, geophysical fluid dynamics, and flows in fluid membranes. This is a joint work with Y. Giga (University of Tokyo) and C. Liu (Penn State University).

September 3rd, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Social Pressure and Group Projects
Speaker: Attendees, Penn State
Location: MB102

Research dating back to the 1950s has demonstrated how difficult it is for an individual to withstand social pressure. In some instances, social pressure can quell correct ideas in favor of incorrect ones. This week, we read an article describing this phenomenon (observed in the laboratory) and discuss strategies to guide students away from it.
Asch, Solomon E. "Opinions and Social Pressure." Scientific American 193.5 (1955): 31-35. Web.

September 4th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Systems of conservation laws in one and two space dimensions (continue)
Speaker: Yuxi Zheng, Penn State
Location: MB216

TBA

September 4th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Galois groups of Mori polynomials, semistable curves and monodromy
Speaker: Yuri Zarhin, Penn State University
Location: MB106

We study the monodromy of a certain class of semistable hyperelliptic curves that was introduced by Shigefumo Mori forty years ago. Using ideas of Chris Hall, we prove that the corresponding monodromy groups are (almost) ``as large as possible".

September 4th, 2014 (01:15pm - 02:30pm)
Seminar: MASS Colloquium
Title: Ramanujan, Fibonacci numbers, and Continued Fractions or Why I Took Zeckendorf's Theorem Along On My Last Trip To Canada
Speaker: George Andrews, Penn State University
Location: MB114

This talk focuses on the famous Indian genius, Ramanujan. One object will be to give some account of his meteoric rise and early death. We shall try to lead from some simple problems involving Fibonacci numbers to a discussion of some of Ramanujan's achievements including some things from his celebrated Lost Notebook.

September 5th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Weighted entropy
Speaker: Yuri Suhov, Penn State/University of Cambridge, UK
Location: MB106

The entropy $h(X)=-\sum_ip_i\log\,p_i$ measures an expected amount of information/uncertainty related to a random variable $X$ taking values $i$ with probabilities $p_i$. The weighted entropy, $h^{\rm w}_\phi(X)$, is defined as $-\sum_i\phi (i)p_i\log\,p_i$ where $\phi (i)\geq 0$ is a weight function representing `utilities' of different values $i$ which we want to take into account. As in the case of a standard entropy, one can introduce conditional and relative weighted entropies; weighted differential entropies can also be defined. In this talk, I will discuss a recent progress in studying weighted entropies and their possible use in various areas.

September 8th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Evolution of social instincts in within- and between-group conflicts
Speaker: Sergey Gavrilets, University of Tennessee (Host: A Belmonte)
Location: MB106

I model the effects of within-group inequality on the evolution of social instincts, i.e. genetically-based propensities and biases that affect the behavior of individuals in social interactions. First, I consider competitive within-group interactions. I identify a novel mechanism for the evolutionary emergence of the "egalitarian syndrome" and leveling coalitions in which one helps the weak against the strong bully. Second, I study a collective action problem in between-group conflicts and show how bullies can dialectically become "altruists". The mechanisms I describe do not require genetic relatedness, reciprocity, reputation, or punishment.

September 8th, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Poisson and compound Poisson asymptotics in conventional and noncoventional setups
Speaker: Yuri Kifer, Hebrew University of Jerusalem
Location: MB114

During last 20-25 years a substantial attention was attracted to the study of numbers of arrivals at small (shrinking) sets by trajectories of dynamical systems during the time intervals inversely proportional to the measure of a set. It seems that the question was originated by Sinai in the framework of the study of distributions of spacings between energy levels of quantum systems. Most of the papers dealt with the symbolic setup of a sequence space Ω with a shift invariant suciently fast mixing probability P where Pitskel, Hirata and Denker showed that when P is a Gibbs shift invariant measure then the numbers of arrivals to shrinking cylindrical neighborhoods of almost all points are asymptotically Poisson distributed. More recently estimates for Poisson approximations were obtained by Abadi and others while Haidn and Vaienti obtained compound Poisson approximations for distributions of numbers of arrivals to shrinking cylindrical neighborhoods of some periodic points. Asymptotics for arrivals to (geometric) balls considering distributions with respect to the SRB measure were studied by Collet, Dolgopyat, Freitas, Freitas, Todd and others. Recently Poisson and compound Poisson limiting behavior in the symbolic situation was extended to numbers of multiple recurrencies (nonconventional setup). In this talk we provide an essentially complete description of possible limiting behaviors of distributions of numbers of multiple recurrencies to shrinking cylinders with respect to ψ-mixing shift invariant measures which is partially new even for the widely studied single (conventional) recurrencies case (most of results are joint with my student Ariel Rapaport).

September 9th, 2014 (01:00pm - 01:50pm)
Seminar: Theoretical Biology Seminar
Title: TBA
Speaker: Brent Doiron, University of Pittsburgh
Location: MB106
September 9th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Randomness, Riesz Capacity, Brownian Motion, and Complexity
Speaker: Jason Rute, Penn State
Location: MB315

- Algorithmic randomness is a topic in computability theory which investigates which paths in a stochastic process behave randomly (with respect to all computable statistical tests). - Riesz capacity is an important concept in potential theory and stochastic processes. It is used to estimate the probability that an n-dimensional Brownian motion hits a given set or is zero on a given set of times. - The a priori complexity KM(x) is a measure of the computational complexity of a finite bit string x. I will present the following result which connects these three subjects. The following are equivalent for t in (0,1]. 1) t is Martin-Löf random with respect to 1/2-Reisz capacity. 2) t is a zero of some Martin-Löf random one-dimensional Brownian motion. 3) sum_n 2^{n/2 - KM(t[0,…,n-1])} < \infty where t[0,…,n-1] is the first n bits of the binary expansion of t. This is joint work with Joseph Miller.

September 9th, 2014 (02:30pm - 03:30pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Topological recurrence: variations and questions
Speaker: Bryna Kra, Northwestern University
Location: MB114

I will give an overview of recurrence, focusing mainly on topological dynamical systems, describing combinatorial interpretations, relations between recurrence in different systems, and methods to formulate finite versions. This is based on joint work with Bernard Host and Alejandro Maass.

September 9th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Metric theory of interval exchange transformations, a survey after Veech
Speaker: Changguang Dong, Penn State
Location: MB216
September 10th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Group Projects Done Right
Speaker: Attendees, Penn State
Location: MB102

Group projects can, of course, be done well... even in a mathematics classroom! This week, we consider ideas set forth in Assessment Practices in Undergraduate Mathematics by the MAA and discuss if they could be used in our classrooms.
Gold, Bonnie, Sandra Keith, and William A. Marion. "Assessment in the Individual Classroom." Assessment Practices in Undergraduate Mathematics. Washington, DC: Mathematical Association of America, 1999. 134-45. Print.

September 11th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: The Strong CM Lifting Problem
Speaker: Taisong Jing, Penn State University
Location: MB106

It is known that an abelian variety over a finite field may not admit a lifting to an abelian variety with complex multiplication in characteristic 0. The question of strong CM lifting (sCML) asks whether we can kill the obstructions to a CM lifting by requiring the whole ring of integers in the CM field act on the abelian variety. I will give counterexamples to question (sCML), prove the answer to question (sCML) is affirmative under certain assumptions on the CM field, and explain some follow-up problems that I have been working on.

September 11th, 2014 (01:15pm - 02:30pm)
Seminar: MASS Colloquium
Title: Introduction to Entropy
Speaker: Yuri Suhov, Penn State / University of Cambridge, UK
Location: MB114
September 15th, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Some mechanical paradoxes and their mathematical explanations
Speaker: Mark Levi, Penn State University
Location: MB114
September 15th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Traveling waves in lattices of oscillators
Speaker: Mark Levi, Penn State University
Location: MB106
September 15th, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Effective Ratner Theorem for ASL(2, R) and the gaps of the sequence \sqrt n modulo 1
Speaker: Ilya Vinogradov, University of Bristol
Location: MB114

Let G=SL(2,\R)\ltimes R2 and Gamma=SL(2,Z)\ltimes Z2. Building on recent work of Strombergsson we prove a rate of equidistribution for the orbits of a certain 1-dimensional unipotent flow of Gamma\G, which projects to a closed horocycle in the unit tangent bundle to the modular surface. We use this to answer a question of Elkies and McMullen by making effective the convergence of the gap distribution of sqrt n mod 1.

September 16th, 2014 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Singular Overpartitions
Speaker: Dr. George Andrews, PSU
Location: MB106
September 16th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: To be announced
Speaker: Adrian Maler, Penn State
Location: MB315
September 17th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Would You Like Some Help?
Speaker: Attendees, Penn State
Location: MB102

Sometimes people are altruistic and sometimes they are not. An ideal class environment is one where students work together and help each other, but what factors lead one person to help another? This week, we read a summary of social psychology literature on this subject and discuss how these findings apply to the classroom.
Myers, David G. "When Do People Help?" Exploring Social Psychology. 6th ed. New York: McGraw-Hill, 1994. 385-93. Print.

September 19th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: A nonconventional local limit theorem
Speaker: Yuri Kifer, Hebrew University
Location: MB106

Local limit theorems have their origin in the classical De Moivre– Laplace theorem and they study the asymptotic behavior as N → ∞ of probabilities having the form P {S_N = k} where S_N = \sum^N_{n=1} F (ξ_n ) is a sum of an integer valued function F taken on i.i.d. or Markov dependent sequence of random variables {ξ_j}. Corresponding results for lattice valued and general functions F were obtained, as well. We extend here this type of results to nonconventional sums of the form S_N = \sum^N_{n=1} F (ξ_n , ξ_{2n} , ..., ξ_{ln} ) and corresponding versions of such results can be obtained for some dynamical systems, as well. This continues the recent line of research studying various limit theorems for such expressions.

September 22nd, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: TBA
Speaker: Martin Schmoll, Clemson University
Location: MB114
September 23rd, 2014 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Arithmetic Properties of Andrews' Singular Overpartitions
Speaker: Dr. James Sellers, PSU
Location: MB106
September 23rd, 2014 (01:00pm - 01:50pm)
Seminar: Theoretical Biology Seminar
Title: TBA
Speaker: Bard Ermentrout, University of Pittsburgh
Location: MB106
September 23rd, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: To be announced
Speaker: Jake Pardo, Penn State
Location: MB315
September 24th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Do As I Say, Not As I Do
Speaker: Attendees, Penn State
Location: MB102

Mathematicians may profess a set of values that differs from what is inferred by their actions. This week, we discuss a paper that looks at discrepancies between what mathematicians value in proofs versus how they teach them.
Lai, Y. & Weber, K. (2014). Factors mathematicians profess to consider when presenting pedagogical proofs. Educational Studies in Mathematics, 85(1), 93-108.

September 26th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: TBA
Speaker: Yuri Suhov, Penn State/University of Cambridge, UK
Location: MB106
September 29th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Blended Atomistic/Continuum Hybrid Methods for crystalline materials
Speaker: Xingjie Li, Brown University (C Liu/X Li)
Location: MB106

We consider two prototypical atomistic-to-continuum coupling methods of blending type: the energy-based and the force-based quasicontinuum methods, with a comprehensive error analysis that is valid in two and three dimensions, for finite many-body interactions (e.g., EAM type), and in the presence of lattice defects (point defects and dislocations). Based on a precise choice of blending mechanism, the error estimates are considered in terms of degrees of freedom. The numerical experiments confirm the theoretical predictions, and demonstrate a superior accuracy of the force-based blending over energy-based blending schemes.

September 30th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: To be announced
Speaker: Jan Reimann, Penn State
Location: MB315