Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, April 7, 2015.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      March 2015             April 2015              May 2015
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1  2  3  4  5  6  7             1  2  3  4                   1  2
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Tuesday, April 7, 2015

11:00 am in 243 Altgeld Hall,Tuesday, April 7, 2015

#### Baez-Dolan Stabilization for Rezk's n-Fold Complete Segal Spaces and the Importance of Left Properness

###### David White   [email] (Denison)

Abstract: We will begin with an overview of an old problem, due to Baez and Dolan, and discuss where in the solution of this problem model category theoretic considerations arise. This requires placing left proper model structures on algebras over certain colored operads. We will discuss how this can be accomplished. Our path will take us through a discussion of model structures on commutative monoids and non-reduced symmetric operads, as well as a new filtration due to Batanin and Berger.

1:00 pm in 347 Altgeld Hall,Tuesday, April 7, 2015

#### A Necessary and Sufficient Condition for Reality of Eigenvalues of Anharmonic Oscillators in the Complex Plane

###### Kwang Shin   [email] (U of West Georgia)

Abstract: All self-adjoint anharmonic oscillators have real eigenvalues only. Self-adjointness is a sufficient condition for real eigenvalues but not a necessary condition. A large class of non-self-adjoint PT-symmetric anharmonic oscillators have real eigenvalues only. In this talk, we will consider all anharmonic oscillators in the complex plane and give a necessary and sufficient condition for classes of anharmonic oscillators in the complex plane to have infinitely many real eigenvalues.

1:00 pm in Altgeld Hall 243,Tuesday, April 7, 2015

#### Marked length rigidity for NPC Euclidean cone metrics

###### Christopher J. Leininger (UIUC Math)

Abstract: Otal proved that for negatively curved Riemannian metrics on compact surfaces, the marked length spectrum---the function which assigns the length of the geodesic representative to each homotopy class of curves---determines the metric up to isometry homotopic to the identity. This was extended to nonpositively curved (NPC) Riemannian metrics by Croke-Fathi-Feldman, and to negatively curved cone metrics by Hersonsky-Paulin. In his thesis, Frazier considered the case of NPC Euclidean cone metrics, and showed that the marked length spectrum distinguishes such metrics from the classes above, but was unable to prove that they could be distinguished by such from each other. In joint work with Anja Bankovic, we prove that NPC Euclidean cone metrics are determined by their marked length spectrum. From the proof, we conjecture that they are (almost) determined by a much coarser invariant, namely the support of the associated Liouville current. I'll explain all the terms and sketch the relatively short proof.

2:00 pm in 347 Altgeld Hall,Tuesday, April 7, 2015

#### Two-species asymmetric exclusion process, critical exponents and height models

###### Birgit Kaufmann (Purdue University)

Abstract: We discuss recent work on the two-species asymmetric exclusion process, partially in collaboration with D. Huse and G. Schuetz. The dynamics of this stochastic process can be described by a master equation with an integrable Hamiltonian. We used the Bethe Ansatz to calculate the dynamical critical exponent. In analogy to the single species exclusion process, we define a height model that reflects the nearest-neighbor interactions of the multi-particle exclusion process and derive the partial differential equations for this model. Depending on the parameters of the model, the dynamics is of KPZ type, diffusive type or a mixture of both. It is interesting to see that these equations also follow directly from the Master equation approach.

3:00 pm in 241 Altgeld Hall,Tuesday, April 7, 2015

#### Cops and Robbers on diameter two graphs

Abstract: The game of Cops and Robbers is a combinatorial game where a set of cops try to catch a robber, while moving along the edges of a fixed graph. The most well-known conjecture in this area states that the number of cops needed is at most the square root of the number of vertices. Even in very special graphs, like graphs of diameter two, the best upper bound is unknown. I will give the best known bound in the diameter two case and describe one possible attempt at obtaining the correct upper bound, show why the proof is incomplete, and where the gaps are that I couldn't fill in.

3:00 pm in 243 Altgeld Hall,Tuesday, April 7, 2015

#### Intersection theory on the moduli of disks

###### Rahul Pandharipande (ETH Zurich)

Abstract: I will discuss a descendent integration theory for open Riemann surfaces. A  careful discussion of the disk case will be given. This leads to a conjecture for the analogues of the KdV and Virasoro constraints (in all genera). Joint work with J. Solomon and R. Tessler.

4:00 pm in 159 Altgeld Hall,Tuesday, April 7, 2015

#### Least-Squares Monte Carlo Approach to the Calculation of Capital Requirements

###### Daniel Bauer (Georgia State University)

Abstract: The calculation of capital requirements for financial institutions usually entails a reevaluation of the company’s assets and liabilities at some future point in time for a (large) number of stochastic forecasts of economic and firm-specific variables. The complexity of this nested valuation problem leads many companies to struggle with the implementation. Relying on a well-known method for pricing non-European derivatives, the current paper proposes and analyzes a novel approach to this computational problem based on least-squares regression and Monte Carlo simulations. We show convergence of the algorithm, we analyze the resulting estimate for practically important risk measures, and we derive optimal basis functions based on spectral methods. Our numerical examples demonstrate that the algorithm can produce accurate results at relatively low computational costs, particularly when relying on the optimal basis functions.

4:00 pm in 245 Altgeld Hall,Tuesday, April 7, 2015

#### Mathematical modeling and simulations and its role in lowering the carbon emissions of trucks

###### Mihai Dorobantu (Eaton Corporation)

Abstract: Heavy Duty trucks consume over 25% of on-road fuel and yet account for less than 7% of vehicles. Drastically reducing that consumption is critical to both bending the curve of CO2 emissions as well as reducing our dependency on foreign oil. Key to transforming an industry as conservative as trucking are mathematical tools enabled by compute power, availability of big data and advances in active controls and optimization. We illustrate the challenges and implications of applied mathematics to vehicle fuel economy in a collection of case studies, ranging from transmissions design to efficient and affordable hybrid systems and full vehicle controls, including human behavior. We will show how efficient controllers are built from a meshing of physics based and data driven models, and examine the potential of parallelizing massive optimization problems associated discrete systems architectures choices.

4:00 pm in 243 Altgeld Hall,Tuesday, April 7, 2015

#### Operator Monotone Functions

###### Li Gao (UIUC Math)

Abstract: In this talk, we will study an important class of functions called operator monotone functions. They are real functions whose extensions to Hermitian matrices preserve order. I will give a sketch proof for Loewner' theorem which characterize operator monotone functions on intervals.