PSU Mark
Eberly College of Science Mathematics Department

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<>August 2015
July 2015
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August 2015
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September 2015
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August 12th, 2015 (10:00am - 12:00pm)
Seminar: Ph.D. Thesis Defense
Title: "Effective Theory of Levy and Feller Processes"
Speaker: Adrian Maler, Adviser: Stephen Simpson, Penn State
Location: MB106

We develop a computational framework for the study of stochastic processes with 'cadlag' (left-limited, right-continuous) modifications, including Levy processes and Feller processes. We prove that a cadlag modification is computable from a representation of the process, and establish other basic results in an effective theory of stochastic processes.

August 13th, 2015 (10:00am - 12:00pm)
Seminar: Ph.D. Thesis Defense
Title: “C*-algebras in Kirillov Theory”
Speaker: Pichkitti Bannangkoon, Adviser: Nigel Higson, Penn State
Location: MB106

In this dissertation, I study connections between C°-algebra theory and the representation theory of simply connected nilpotent Lie groups, specifically the Kirillov theory. If G is a simply connected nilpotent Lie group, then Kirillov’s famous theorem gives an explicit bijection between the set of equivalence classes of unitary irreducible representations of G and the set of coadjoint orbits of G in g, the dual of the Lie algebra of G. Inspired by this, and by the Plancherel theorem, I introduce two new C°-algebras. The first is an algebra of operators on L2pGq and the second is an algebra of operators on L2pg°q. I formulate the conjecture that they are isomorphic, prove the conjecture in the case of Heisenberg group (which is the crucial building block for general nilpotent Lie groups) and examine the prospects for the conjecture in other cases.

August 14th, 2015 (10:00am - 12:00pm)
Seminar: Ph.D. Thesis Defense
Title: "Quantization of Affine Coadjoint Orbits"
Speaker: Guangzhong Peng, Adviser: Paul Baum/Nigel Higson, Penn State
Location: MB106

Using twisted equivariant K-homology, E. Meinrenken defined the quantization of a q-Hamiltonian space as the pushforward of the fundamental class by a Morita morphism and obtained an element in the Verlinde algebra. This dissertation explains a different way to obtain the quantization of a Hamiltonian loop group space.

August 17th, 2015 (01:00pm - 03:00pm)
Seminar: Ph.D. Thesis Defense
Title: "On the Quantization of Coadjoint Orbits via the Positivity of Kirillov's Character Formula"
Speaker: Ehssan Khanmohammadi, Adviser: Nigel Higson, Penn State
Location: MB106

Kirillov proved his character formula for simply connected nilpotent Lie groups in 1962 and conjectured its universality. The validity of this conjecture has been verified for some other classes of Lie groups, most notably for the case of tempered representations of reductive Lie groups by Rossmann. In this dissertation we explain how Kirillov's character formula can be used in the quantization of coadjoint orbits. First we prove a positivity property of Kirillov's character formula for some classes of Lie groups, including nilpotent Lie groups, which possess real polarizing subgroups. Then we use this positivity property to construct group representations following the ideas of Gelfand, Naimark, and Segal. Finally we discuss several approaches to proving positivity in the absence of real polarizations.

August 24th, 2015 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Introduction to applied math courses
Speaker: Various speakers
Location: MB114
August 24th, 2015 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Global Riemann Solver for Gas Flooding in Reservoir Simulation
Speaker: Wen Shen, Penn State
Location: MB106

In this talk we consider the model for gas flooding with three component. The resulting model is a 2 × 2 system of conservation law. The model is known to be non-hyperbolic, with various degeneracies. These include a curve and an area of linearly degeneracy, two curves of parabolic degeneracy. We present a construction of the global Riemann Solver, which takes advantage of the under- lining splitting property of the thermo-dynamics from the hydro-dymanics. This is a joint work with S. Khorsandi and R. Johns, both from Department of Energy and Mineral Engineering, Penn State University.

August 25th, 2015 (01:30pm - 02:20pm)
Seminar: Theoretical Biology Seminar
Title: Note: special Applied Algebra talk (not TBS). Computing Galois groups numerically with Bertini.
Speaker: Jose Israel Rodriguez, Notre Dame
Location: MB106

Galois groups are an important part of number theory and algebraic geometry. To a parameterized system of polynomial equations one can associate a Galois group whenever the system has k (finitely many) nonsingular solutions generically. The Galois group of a parameterized system is a subgroup of the symmetric group on k elements. Using random monodromy loops it has been shown how to compute the Galois group when it is the full symmetric group. In this talk we show how to compute Galois groups that are not the full symmetric group. We conclude with an implementation using Bertini.m2, an interface to the numerical algebraic geometry software Bertini through Macaulay2. This is joint work with Jon Hauenstein and Frank Sottile.

August 25th, 2015 (03:00pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: Self-Assembly in Colloidal Systems: New Insights through Novel Algorithms
Speaker: Erik Luijten, Northwestern University
Location: MB216

Suspensions of colloidal particles are widely studied as prototypical systems displaying self-assembly. I will demonstrate how efficient simulation algorithms can yield new insights into physical phenomena observed in these systems. Specifically, I will focus on (1) a general Monte Carlo algorithm for complex fluids that is rejection-free, irrespective of the interactions involved, and (2) a boundary-element method that permits the dynamic computation of induced dielectric effects. Both algorithms make it possible to uncover explanations for striking experimental observations.

August 26th, 2015 (03:30pm - 05:30pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: Computing Galois groups numerically with Bertini.
Speaker: Jose Israel Rodriguez. NOTE THE TIME/ROOM CHANGE: Tuesday 01:30-02:20 in MB106, University of Notre Dame
Location: MB315

Galois groups are an important part of number theory and algebraic geometry. To a parameterized system of polynomial equations one can associate a Galois group whenever the system has k (finitely many) nonsingular solutions generically. The Galois group of a parameterized system is a subgroup of the symmetric group on k elements. Using random monodromy loops it has been shown how to compute the Galois group when it is the full symmetric group. In this talk we show how to compute Galois groups that are not the full symmetric group. We conclude with an implementation using Bertini.m2, an interface to the numerical algebraic geometry software Bertini through Macaulay2. This is joint work with Jon Hauenstein and Frank Sottile.

August 26th, 2015 (06:00pm - 07:00pm)
Seminar: GTA and Instructor Training
Title: "Teaching Mathematics at Penn State"
Speaker: James Sellers, Professor and Associate Head of Undergraduate Mathematics, Penn State
Location: MB114
August 27th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Organisational Meeting
Speaker: All, PSU
Location: MB106

Meet for lunch at 11:45

August 27th, 2015 (11:15am - 12:29pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Introduction/Organizational Meeting
Speaker: Attendees, Penn State
Location: MB102

The Teaching Mathematics Discussion Group is designed to be an open forum for those of us to teach mathematics to ask questions, discuss best practices, and evaluate research pertaining to mathematics education. We may also feature guest speakers or workshops in specific skill areas. The group is open to anyone and you do not have to attend every week to participate. Simply show up for the week when the topics sound interesting or applicable to you! This week, we will be brainstorming ideas for the coming sessions, so just bring a friendly face and any questions you may have about teaching mathematics. These can be big or small, philosophical or practical. We are open to all ideas. Hope to see you there!

August 27th, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Noncommutative Geometry 101: Operators and symbols
Speaker: Nigel Higson, Penn State
Location: MB106

I shall give two lectures introducing some of the ideas that appear in the research of Penn State's noncommutative geometry group. In the first I shall discuss differential and Hilbert space operators, and various sorts of "symbols" that can be attached to them. In the second I shall examine how the general theory applies to Sturm-Liouville operators on a half-line, following some remarkable early work Hermann Weyl that has proved to be very influential in representation theory.

August 28th, 2015 (03:00pm - 04:30pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Numerical methods for fine-scale petroleum reservoir simulation
Speaker: Chensong Zhang, Chinese Academy of Sciences
Location: MB315

Computer simulation is widely used by petroleum engineers to understand oil recovery mechanisms. We will first briefly review a few mathematical models for petroleum reservoir simulation. Then we focus on a general compositional model and develop a fully-implicit method as well as effective preconditioners for solving the Jacobian systems. We will also discuss efficient parallel implementation of the proposed preconditioners on different platforms. The accuracy, robustness, and parallel scalability of the parallel simulator are then validated using large-scale black oil benchmark problems.

August 28th, 2015 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Markov processes in a random environment
Speaker: Yuri Suhov, Penn State University
Location: MB106

Abstract. We propose a construction of a Markov process (MP) in a (Markovian) random environment. (I am not 100 percent sure: may be some special cases/elements of this constructions can be found in the existing literature.) A feature of this construction is that it allows an invariant measure (IM) which is naturally built from IMs for the basic MPs and IMs for the MP (or (MPs)) describing the dynamics of state of environment (SE). In general tems, the generator of the combined process is obtained as a sum of generators for components (with non-commuting summands). This construction gives quite spectacular results for some interesting examples: Jackson network, simple exclusion, Ornstein--Uhlenbeck. (The latter is related to the concept of stochastic volatility in Math Finance.) In the course of presentation, I will not assume any special knowledge from the theory of Markov processes or their applications. However, exposure to basic probabilistic concepts would make understanding easier.

August 31st, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Slow entropy for smooth flows on surfaces
Speaker: Adam Kanigowski, The Pennsylvania State University
Location: MB114

We will discuss slow entropy in the class of mixing smooth flows on surfaces. As a consequence we will find countably many non-isomorphic (disjoint) smooth flows. Moreover, we will show that they don't have finite rank.