Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, December 4, 2018.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, December 4, 2018

11:00 am in 345 Altgeld Hall,Tuesday, December 4, 2018

The Equivariant Spanier-Whitehead dual of the Lubin-Tate spectrum Part 1

Vesna Stojanoska (UIUC)

Abstract: In a series of two talks, I will address the question of determining the K(n)-local Spanier-Whitehead dual of the Lubin-Tate spectrum, equivariantly with respect to the action of the Morava stabilizer group. In the first talk, I will focus on the abstract dualizing module, and introduce the Linearization Conjecture, which makes a more tangible (and linear) guess for what this spectrum should be. In the second talk, I will discuss a proof of the Linearization Conjecture, when restricted to small finite subgroups of the Morava stabilizer. This is work in progress, joint with Beaudry, Goerss, and Hopkins. (Note: the second talk will be independent from the first.)

1:00 pm in 347 Altgeld Hall,Tuesday, December 4, 2018

Unconditional uniqueness for the derivative nonlinear Schrodinger equation

Razvan Mosincat (The University of Edinburgh)

Abstract: We consider the initial-value problem for the derivative nonlinear Schrödinger equation (DNLS) on the real line. We implement an infinite iteration of normal form reductions (namely, integration by parts in time) and reformulate a gauge-equivalent equation in terms of an infinite series of multilinear terms. This allows us to show the unconditional uniqueness of solutions to DNLS in an almost end-point space. This is joint work with Haewon Yoon (National Taiwan University).

2:00 pm in 345 Altgeld Hall,Tuesday, December 4, 2018

Convergence of Trapezoid Rule to Rough Integrals

Zachary Selk (Purdue University)

Abstract: Rough paths offer the only notion of solution to SDEs driven by non-semimartingales with poor total $p$-variation such as fractional Brownian motion with Hurst index $H<1/2$. Rough paths further offer a notion of pathwise solution to SDEs classically handled by Itô calculus. Applications include large deviations theory, volatility models in finance, filtering theory, and SPDEs. If one can define certain iterated integrals, they act as a sort of "correction term" in Riemann sums, restoring convergence to classically divergent sums. These corrected Riemann sums are known as rough integrals. However these correction terms are unnatural. We prove for a general class of multidimensional Gaussian processes the convergence of the trapezoid rule to these corrected Riemann sums. The trapezoid rule doesn't have any correction terms so is in some sense more natural. Joint work with Yanghui Liu and Samy Tindel.

2:00 pm in 243 Altgeld Hall,Tuesday, December 4, 2018

On Vertex-Disjoint Chorded Cycles

Derrek Yager (Illinois Math)

Abstract: In 1963, Corrádi and Hajnal proved that for all \( k \geq 1 \), any graph with \( |G| \geq 3k\) and \( \delta(G) \geq 2k \) has \( k \) vertex-disjoint cycles. In 2010, Chiba, Fujita, Gao, and Li proved that for all \( k \geq 1 \), any graph with \( |G| \geq 4k \) and minimum Ore-degree at least \( 6k - 1 \) contains \( k \) vertex-disjoint chorded cycles. In 2016, Molla, Santana, and Yeager refined this to characterize all graphs with \( |G| \geq 4k\) and minimum Ore-degree at least \( 6k - 2 \) that do not have \( k \) vertex-disjoint chorded cycles. We further refine this to characterize such graphs with Ore-degree at least \( 6k - 3\) that do not have \( k \) vertex-disjoint chorded cycles.