Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, September 12, 2017.

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Tuesday, September 12, 2017

11:00 am in 345 Altgeld Hall,Tuesday, September 12, 2017

The cooperations algebra for the second truncated Brown-Peterson spectrum

Dominic Culver (UIUC math)

Abstract: In the 1980s Mahowald and Mahowald-Lellmann studied the Adams spectral sequence for the sphere based on the connective real K-theory spectrum. In particular, it was used to study the height 1 telescope conjecture at the prime 2 and to perform low dimensional calculations of the stable homotopy groups of the sphere. Motivated by this, Mahowald proposed using the connective spectrum of topological modular forms to study height 2 telescope phenomena and to perform calculations. This requires understanding the cooperations algebra for tmf, and work of Behrens, Ormsby, Stapleton, and Stojanoska give partial calculations of this cooperations algebra. In this talk, I will talk discuss the problem of computing the cooperations algebra for a variant of tmf, which is sometimes referred to as BP<2>.

1:00 pm in 345 Altgeld Hall,Tuesday, September 12, 2017

The complexity of the classification problem in ergodic theory

Martino Lupini (Caltech Math)

Abstract: Classical results in ergodic theory due to Dye and Ornstein–Weiss show that, for an arbitrary countable amenable group, any two free ergodic measure-preserving actions on the standard atomless probability space are orbit equivalent, i.e. their orbit equivalence relations are isomorphic. This motivates the question of what happens for nonamenable groups. Works of Ioana and Epstein showed that, for an arbitrary countable amenable group, the relation of orbit equivalence of free ergodic measure-preserving actions on the standard probability space has uncountably many classes. In joint work with Gardella, we strengthen these conclusions by showing that such a relation is in fact not Borel. This builds on previous work of Epstein, Tornquist, and Popa, and answers a question of Kechris.

2:00 pm in 347 Altgeld Hall,Tuesday, September 12, 2017

On the fast convergence of random perturbations of the gradient flow

Wenqing Hu (Missouri S&T)

Abstract: We consider in this talk small random perturbations (of multiplicative noise type) of the gradient flow. We rigorously prove that under mild conditions, when the potential function is a Morse function with additional strong saddle condition, the perturbed gradient flow converges to the neighborhood of local minimizers in O(ln(\eps^{−1})) time on the average, where \eps>0 is the scale of the random perturbation. Under a change of time scale, this indicates that for the diffusion process that approximates the stochastic gradient method, it takes (up to logarithmic factor) only a linear time of inverse stepsize to evade from all saddle points and hence it implies a fast convergence of its discrete--time counterpart.

3:00 pm in 243 Altgeld Hall,Tuesday, September 12, 2017

To Be Announced

Chris Dodd (UIUC)

3:00 pm in 345 Altgeld Hall,Tuesday, September 12, 2017

Asymptotic theory of parametric inference for ruin probability under Levy insurance risks

Yasutaka Shimizu (Department of Applied Mathematics, Waseda University)

Abstract: The aim of this paper is to construct the confidence interval of the ultimate ruin probability under the insurance surplus driven by a Levy process. Assuming a parametric family for the Levy measures, we estimate the parameter from the surplus data, and estimate the ruin probability via the "delta method". However the asymptotic variance includes the derivative of the ruin probability with respect to the parameter, which is not generally given explicitly, and the confidence interval is not straightforward even if the ruin probability is well estimated. This paper gives the Cramer-type approximation for the derivative, and gives an asymptotic confidence interval of ruin probability.