Department of

Mathematics


Seminar Calendar
for events the day of Thursday, February 20, 2020.

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Thursday, February 20, 2020

11:00 am in 241 Altgeld Hall,Thursday, February 20, 2020

The Third Moment of Quadratic L-Functions

Ian Whitehead (Swarthmore College)

Abstract: I will present.a smoothed asymptotic formula for the third moment of Dirichlet L-functions associated to real characters. Beyond the main term, which was known, the formula has an unexpected secondary term of size $X^{3/4}$ and an error of size $X^{2/3}$. I will give background on the multiple Dirichlet series techniques that motivated this result. And I will describe the new ideas about local and global multiple Dirichlet series that made the final, sieving step in the proof possible. This is joint work with Adrian Diaconu.

2:00 pm in 347 Altgeld Hall,Thursday, February 20, 2020

Distribution of eigenvalues of random matrices (part II)

Peixue Wu (UIUC Math)

Abstract: Last time we proved the classical Wigner's semicircular law for Wigner matrix. This time I will state a dynamical version of the semicircular law, which implies the classical Wigner's semicircular law. Our main tool will be stochastic analysis.

2:00 pm in 243 Altgeld Hall,Thursday, February 20, 2020

Around the Folds

Kirsi Peltonen (Aalto University, Finland)

Abstract: We will discuss about various ways to use origami and folding as a multidisciplinary tool in research and education. Some ongoing projects funded by Academy of Finland and Ministry of Education and Culture with theoretical and practical goals are described. The slides of the talk as a pdf-file can be obtained by clicking on the name of the speaker above.

4:00 pm in 245 Altgeld Hall,Thursday, February 20, 2020

Data-driven methods for model identification and parameter estimation of dynamical systems

Niall Mangan   [email] (Northwestern University)

Abstract: Inferring the structure and dynamical interactions of complex systems is critical to understanding and controlling their behavior. I am interested in discovering models from the time-series in order to understand biological systems, material behavior, and other dynamical systems. One can frame the problem as selecting which interactions, or model terms, are most likely responsible for the observed dynamics from a library of possible terms. Several challenges make model selection and parameter estimation difficult including nonlinearities, varying parameters or equations, and unmeasured state variables. I will discuss methods for reframing these problems so that sparse model selection is possible including implicit formulation and data clustering. I will also discuss preliminary results for parameter estimation and model selection for deterministic and chaotic systems with hidden or unmeasured variables. We use a variational annealing strategy that allows us to estimate both the unknown parameters and the unmeasured state variables.

4:00 pm in 243 Altgeld Hall,Thursday, February 20, 2020

Variable-order time-fractional partial differential equations: modeling and analysis

Hong Wang (University of South Carolina)

Abstract: Fractional partial differential equations (FPDEs) provide more accurate descriptions of anomalously diffusive transport of solute in heterogeneous porous media than integer-order PDEs do, because they generate solutions with power law (instead of exponentially) decaying tails that were observed in field tests. However, solutions to time-fractional PDEs (tFPDEs) have nonphysical singularity at the initial time t=0, which does not seem physically relevant to anomalously diffusive transport they model and makes many error estimates to their numerical approximations in the literature that were proved under the full regularity assumption of the true solutions in appropriate. The reason lies in the incompatibility between the nonlocality of the power law decaying tail of the solutions and the locality of the initial condition. But there is no consensus on how to correct the nonphysical behavior of tFPDEs. We argue that the order of a physically correct tFPDE model should vary smoothly near the initial time to account for the impact of the locality of the initial condition. Moreover, variable-order tFPDEs themselves also occur in a variety of applications. However, rigorous analysis on variable-order tFPDEs is meager. We outline the proof of the wellposedness and smoothing properties of tFPDEs. More precisely, we prove that their solutions have the similar regularities to their integer-order analogues if the order has an integer limit at the initial time or have the same singularity near the initial time as their constant-order analogues otherwise.