Department of

# Mathematics

Seminar Calendar
for Analysis Seminar events the year of Friday, February 14, 2020.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2020          February 2020            March 2020
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4                      1    1  2  3  4  5  6  7
5  6  7  8  9 10 11    2  3  4  5  6  7  8    8  9 10 11 12 13 14
12 13 14 15 16 17 18    9 10 11 12 13 14 15   15 16 17 18 19 20 21
19 20 21 22 23 24 25   16 17 18 19 20 21 22   22 23 24 25 26 27 28
26 27 28 29 30 31      23 24 25 26 27 28 29   29 30 31



Thursday, January 23, 2020

2:00 pm in 243 Altgeld Hall,Thursday, January 23, 2020

#### Free Banach Lattices

###### Vladimir Troitsky (University of Alberta)

Abstract: A free Banach lattice is the largest Banach lattice generated by a set of given cardinality. Similarly, a Banach lattice $X$ is free over a Banach space $E$ if $X$ is the largest Banach lattice which contains $E$ as a subspace and is generated by it. Equivalently, every bounded linear operator from $E$ to an arbitrary Banach lattice $Y$ extends to a lattice homomorphism from $X$ to $Y$ of the same norm. In the talk, we will discuss several methods of generating free vector and Banach lattices.

Friday, January 24, 2020

3:00 pm in 347 Altgeld Hall,Friday, January 24, 2020

#### Organizational Meeting

###### Kesav Krishnan (UIUC Math)

Abstract: This organizational meeting will be to decide on a schedule of speakers. All are welcome

Friday, January 31, 2020

3:00 pm in 347 Altgeld Hall,Friday, January 31, 2020

#### Indroduction to Non Commutative Probability

###### Kesav Krishnan (UIUC Math)

Abstract: In this talk I will introduce Non Commutative Probability Theory, and highlight some of its uses in classical Probability, such as the study of random matrices. In particular, motivation of Wigner's semi-circle law as the non commutative analog of the Central Limit Theorem.

Friday, February 7, 2020

3:00 pm in 347 Altgeld Hall,Friday, February 7, 2020

#### Indroduction to Non Commutative Probability Part 2

###### Kesav Krishnan (UIUC Math)

Abstract: I will continue the talk from last friday, on the Introduction to Non Commutative Probability. In this talk, I will focus on limit laws, in particular the non commutative CLT and the universality of the semi-circle law.

Thursday, February 13, 2020

2:00 pm in 243 Altgeld Hall,Thursday, February 13, 2020

#### Asymptotic dimension and coarse embeddings in the quantum setting

###### Alejandro Chavez-Dominguez (University of Oklahoma)

Abstract: We generalize the notions of asymptotic dimension and coarse embeddings, from metric spaces to quantum metric spaces in the sense of Kuperberg and Weaver. We show that the quantum asymptotic dimension behaves well with respect to several natural operations, and in particular with respect to quantum coarse embeddings. Moreover, in analogy with the classical case, we prove that a quantum metric space that equi-coarsely contains a sequence of quantum expanders must have infinite asymptotic dimension. This is done by proving a vertex-isoperimetric inequality for quantum expanders, based upon a previously known edge-isoperimetric one. Joint work with Andrew Swift.

Friday, February 14, 2020

3:00 pm in 347 Altgeld Hall,Friday, February 14, 2020

#### An Introduction to $L^2$ Cohomology

###### Gayana Jayasinghe (UIUC Math)

Abstract: We'll see how we can construct quasi isometry invariants and some conformal invariants with function spaces and operators on manifolds (and some more general spaces), and how we can use analysis to study geometric structures

Thursday, February 20, 2020

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.

Friday, February 21, 2020

2:00 pm in 447 Altgeld Hall,Friday, February 21, 2020

#### Novikov conjecture for groups generated by coarsely embeddable groups under extensions and admissible limits

###### Zhizhang Xie (Texas A&M)

Abstract: I will talk about some recent work on the strong Novikov conjecture for groups generated by coarsely embeddable groups under extensions and admissible limits. Here we say a group $G$ is an admissible limit of a family of groups $\{ G_i \}$ if the following is satisfied: for any finite subset $F$ of $G$, there exists $n$ such that the preimage of $F$ in $G_i$ injects into $G$ for all $i > n$. This talk is based on my joint work with Jintao Deng and Guoliang Yu.

Friday, February 28, 2020

3:00 pm in 347 Altgeld Hall,Friday, February 28, 2020

#### Eigenvalues on Forms

###### Xiaolong Han (UIUC Math)

Abstract: Recently there has been a growing interest in eigenvalues on forms. It is much more complicated than eigenvalues on functions but can detect finer geometry. It has applications in detecting length of axes of John ellipsoid of convex body, relating Monopole Floer homology to hyperbolic geometry, and commutator length in hyperbolic geometry. In this talk we will show some basic theory and definitions for eigenvalues on forms, and then provide some intuition for the geometry and applications.

Thursday, March 12, 2020

2:00 pm in 243 Altgeld Hall,Thursday, March 12, 2020

#### Projective and affine equivalence in sub-Riemannian geometry: integrability and separation of variables phenomena

###### Igor Zelenko (Texas A&M)

Abstract: Two sub-Riemannian metrics are called projectively equivalent if they have the same geodesics up to a reparameterization and affinely equivalent if they have the same geodesics up to affine reparameterization. In the Riemannian case both equivalence problems are classical: local classifications of projectively and affinely equivalent Riemannian metrics were established by Levi-Civita in 1898 and Eisenhart in 1923, respectively. In particular, a Riemannian metric admitting a nontrivial (i.e. non-constant proportional) affinely equivalent metric must be a product of two Riemannian metrics i.e. certain separation of variable occur, while for the analogous property in the projectively equivalent case a more involved (twisted") product structure is necessary. The latter is also related to the existence of sufficiently many commuting nontrivial integrals quadratic with respect to velocities for the corresponding geodesic flow. We will describe the recent progress toward the generalization of these classical results to sub-Riemannian metrics. In particular, we will discuss genericity of metrics that can uniquely, up to a constant multiple, be recovered from the knowledge of their geodesics as unparametrized curves and the separation of variables phenomenon on the level of linearization of geodesic flows (i.e. on the level of Jacobi curves) for metrics that admit non-constantly proportional affinely equivalent metrics. The original motivation for this type of problems comes by a widely accepted opinion in Neuroscience that typical human movements optimality certain cost, so the original question is how to recover this cost from the sufficient big collection of typical movements. Although the model describing human movements are not sub-Riemannian, the sub-Riemannian setting seems to be an interesting and rich case study. The talk is based on the collaboration with Frederic Jean (ENSTA, Paris) and Sofya Maslovskaya (INRIA, Sophya Antipolis).

Thursday, April 2, 2020

2:00 pm in 243 Altgeld Hall,Thursday, April 2, 2020

#### To Be Announced

###### Valentino Magnani (University of Pisa)

Thursday, April 9, 2020

2:00 pm in 243 Altgeld Hall,Thursday, April 9, 2020