Department of

Mathematics


Seminar Calendar
for events the week of Thursday, April 25, 2019.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, April 22, 2019

3:00 pm in 343 Altgeld Hall,Monday, April 22, 2019

Complex structures on Real vector bundles

Abhra Abir Kundu (UIUC Math)

Abstract: In this talk, I will state the first and the second obstruction to having a stable complex structure on a real vector bundle. I will then show how one can go from stable complex structure to complex structure. And, if time permits, I will try to sketch how the second obstruction can be expressed as a secondary cohomology operation.

5:00 pm in Altgeld Hall,Monday, April 22, 2019

The complete logarithmic Sobolev inequality and Ricci curvature.

Haojian Li (UIUC)

Abstract: Today we are going to prove the main theorem and show how the lower bound of Ricci curvature get involved with algebra.

Tuesday, April 23, 2019

1:00 pm in 347 Altgeld Hall,Tuesday, April 23, 2019

On Hardy-Rellich-type inequalities

Fritz Gesztesy (Baylor University)

Abstract: We will illustrate how factorizations of singular, even-order partial differential operators yield an elementary approach to classical inequalities of Hardy-Rellich-type. More precisely, using this factorization method, we will derive a general inequality and demonstrate how particular choices of the parameters contained in this inequality yield well-known inequalities, such as the classical Hardy and Rellich inequalities, as special cases. Actually, other special cases yield additional and apparently less well-known inequalities. We will indicate that our method is quite flexible when it comes to a variety of generalized situations involving the inclusion of remainder terms and higher-order operators. If time permits, we might illustrate a very recent new and most elementary proof in the one-dimensional context. This talk will be accessible to students. This is based on joint work with Lance Littlejohn, Isaac Michael, and Michael Pang.

1:00 pm in 345 Altgeld Hall ,Tuesday, April 23, 2019

Expansions of the real field which does not introduce new smooth functions

Alex Savatovsky (Universität Konstanz)

Abstract: We will give some conditions under which an expansion of the real field does not define new smooth functions. We will give a very rough sketch of the proof and discuss generalizations.

2:00 pm in 243 Altgeld Hall,Tuesday, April 23, 2019

Partitions of hypergraphs under variable degeneracy constraints

Michael Stiebitz (TU Ilmenau)

Abstract: We use the concept of variable degeneracy of a hypergraph in order to unify the seemingly remote problems of determining the point partition numbers and the list chromatic number of hypergraphs. Our hypergraphs may have multiple edges, but no loops. Given a hypergraph $G$ and a sequence $f = (f_1, f_2, \dots , f_p)$ of $p \ge 1$ vertex functions $f_i : V(G) → \mathbb N_0$ such that $f_1(v) + f_2(v) + · · · + f_p(v) \ge d_G(v)$ for all $v \in V(G)$, we want to find a sequence $(G_1, G_2, \dots , G_p)$ of vertex disjoint induced subhypergraphs containing all vertices of $G$ such that each hypergraph G_i is strictly $f_i$-degenerate, that is, for every non-empty subhypergraph $G' \subseteq G_i$ there is a vertex $v \in V (G')$ such that $d_{G'}(v) < f_i(v)$. The main result says that such a sequence of hypergraphs exists if and only if $(G, f)$ is not a so-called hard pair. Hard pairs form a recursively defined family of configurations, obtained from three basic types of configurations by the operation of merging a vertex. For simple graphs this result was obtained by O. Borodin, A. V. Kostochka, and B. Toft in 2000. As a simple consequence of our result we obtain a Brooks-type result for the list chromatic number of digraphs due to A. Harautyunyan and B. Mohar. In a digraph coloring the aim is to color the vertices of a directed graph $D$ such that each color class induces an acyclic digraph of $D$, that is, a directed graph not containing any directed cycle. This coloring concept was introduced by V. Neumann-Lara in the 1980s.

3:00 pm in 243 Altgeld Hall,Tuesday, April 23, 2019

Virtual Euler characteristics of Quot scheme of surfaces

Rahul Pandharipande (ETH Zurich)

Abstract: Let S be a nonsingular projective surface. Quot schemes of quotients on S with supports of dimensions 0 and 1 always have 2-term obstruction theories (and therefore also have natural virtual fundamental classes). I will explain what we know about the virtual Euler characteristics in this theory: theorems, conjectures, and a lot of examples. Joint work with Dragos Oprea.

4:00 pm in 245 Altgeld Hall,Tuesday, April 23, 2019

The challenge of modeling dryland vegetation pattern formation using ideas from dynamical systems

Mary Silber (University of Chicago)

Abstract: A beautiful example of spontaneous pattern formation appears in the distribution of vegetation in some dry-land environments. Examples from Africa, Australia and the Americas reveal that vegetation, at a community scale, may spontaneously form into stripe-like bands, alternating with striking regularity with bands of bare soil, in response to aridity stress. A typical length scale for such patterns is 100 m; they are readily surveyed by modern satellites (and explored from your armchair in Google maps). These ecosystems represent some of Earth’s most vulnerable under threats to desertification, and some ecologists have suggested that the patterns, so easily monitored by satellites, may have potential as early warning signs of ecosystem collapse. I will describe efforts based in simple mathematical models, inspired by decades of physics research on pattern formation, to understand the morphology of the patterns, focusing particularly on topographic influences. I will take a critical look at the role of mathematical models in developing potential remote probes of these ecosystems. How does mathematical modeling influence what we see? Does it suggest what we should monitor? Could it lead us astray?

Wednesday, April 24, 2019

3:00 pm in 2 Illini Hall,Wednesday, April 24, 2019

Intersection Theory V-Intersection Products

Sungwoo Nam (Illinois Math)

Abstract: In this talk, we will see the important construction of deformation to the normal cone, which is an analog of the tubular neighborhood theorem in algebraic geometry. Using this, we will define intersection product with a regular codimension d subvariety, generalizing intersection with a divisor introduced in the second talk. Time permitting, we will see how to understand the number 3264 from the intersection theory point of view.

3:00 pm in 243 Altgeld Hall,Wednesday, April 24, 2019

To Be Announced

Mary Silber (University of Chicago, Statistics)

4:00 pm in 245 Altgeld Hall,Wednesday, April 24, 2019

Disable the Label: A Dialogue on Ableism

TBA (Office of Inclusion & Intercultural Relations)

Abstract: Disable the Label: A Dialogue on Ableism examines issues related to disability and ableism, including an introduction to accommodations, how our physical, social, and cultural environment defines disability, and how to be an ally to people with disabilities. Participants will leave the workshop with resources to continue the conversation about disability justice.

Thursday, April 25, 2019

11:00 am in 241 Altgeld Hall,Thursday, April 25, 2019

Local models for potentially crystalline deformation rings and the Breuil-Mézard conjecture

Stefano Morra (Paris 8)

Abstract: Available at https://faculty.math.illinois.edu/~pballen/stefano-morra-abstract.pdf

12:00 pm in 243 Altgeld Hall,Thursday, April 25, 2019

Mirzakhani's curve counting

Viveka Erlandsson (U Bristol)

Abstract: Mirzakhani proved two theorems about the asymptotic growth of the number of curves in a mapping class group orbit on a surface: one for simple curves and another for general curves. In this talk I will explain how to derive her second theorem from the one about simple curves. Time permitting, I will explain why similar methods can be used to also give a proof for the theorem about simple curves, hence giving a new (and very different) proof of both theorems.

2:00 pm in 243 Altgeld Hall,Thursday, April 25, 2019

Classification of irreversible and reversible operator algebras

Adam Dor-On (UIUC Math)

Abstract: C*-algebras have been studied quite extensively in the literature, especially in an attempt to classify them using K-theory. One canonical example is classification of Cuntz-Krieger algebras of a directed graph where K-theory was shown to coincide with Bowen-Franks groups of the subshift associated to the graph. On the other hand, non-self-adjoint operator algebras have been used to encode one-sided processes such as continuous maps on a compact space, stochastic matrices and graphs in their own right. In this talk we will survey results from both irreversible and reversible classification, and uncover a beautiful hierarchy of classification results for irreversible and reversible operator algebras.

2:00 pm in 347 Altgeld Hall,Thursday, April 25, 2019

Coupling and its applications

Peixue Wu (UIUC Math)

Abstract: I will define what is coupling. The beginning example is the transport problem, which leads to the concepts of optimal coupling and probability distance. We will also talk about applications of coupling to study ergodicity, gradient estimate and Harnack's inequality for Markov processes.

4:00 pm in 245 Altgeld Hall,Thursday, April 25, 2019

Spring Department Faculty Meeting

Abstract: The Spring Department Faculty Meeting will be held at 4 p.m. in 245 Altgeld Hall, followed by a reception in 239 Altgeld Hall.

Friday, April 26, 2019

4:00 pm in 345 Altgeld Hall ,Friday, April 26, 2019

On generic monothetic subgroups of Polish groups

Dakota Ihli (UIUC Math)

Abstract: Given a Polish group $G$, what can be said about the subgroup $\overline{\left\langle g \right\rangle}$ for the generic element $g \in G$? In this talk we will discuss progress and open problems in this area. Special emphasis will be given on the group of measure-preserving automorphisms of the unit interval.

4:00 pm in 145 Altgeld Hall,Friday, April 26, 2019

Relatively hyperbolic groups and Dehn fillings

Heejoung Kim (UIUC)

Abstract: Geometric group theory has been studied extensively since Gromov introduced the notion of a hyperbolic group. For instance, the fundamental group of a hyperbolic surface is a hyperbolic group, but not the fundamental group of a cusped hyperbolic 3-manifold. From this motivating example, we consider a generalization of a hyperbolic group, called a relatively hyperbolic group. On the other hand, Thurston's Dehn filling theorem states that one can obtain further hyperbolic 3-manifolds from a given cusped hyperbolic 3-manifold. Groves and Manning extended Thurston's Dehn filling theorem to the context of relatively hyperbolic groups. In this talk, we will discuss hyperbolic groups, relatively hyperbolic groups, and the group-theoretic analog of Thurston's Dehn filling theorem in the context of relatively hyperbolic groups.