Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, October 27, 2015.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, October 27, 2015

11:00 am in 243 Altgeld Hall,Tuesday, October 27, 2015

#### E_n cells and homological stability

###### Sander Kupers (Stanford)

Abstract: When studying objects with additional algebraic structure, e.g. algebras over an operad, it can be helpful to consider cell decompositions adapted to these algebraic structures. I will talk about joint work with Jeremy Miller on the relationship between E_n-cells and homological stability. Using this theory, we prove a local-to-global principle for homological stability, as well as give a new perspective on homological stability for various spaces including symmetric products and spaces of holomorphic maps.

#### Dynamics and Cauchy-Riemann Geometry

###### Ilya Kossovskiy (Univ. of Vienna)

Abstract: From the point of view of Complex Analysis, Cauchy-Riemann (CR) Geometry is a tool for studying holomorphic functions of several variables. From the point of view of Differential Geometry, CR Geometry lies in the framework of Cartan's moving frame method. Finally, CR Geometry is a tool for studying properties of solutions of linear Partial Differential Equations, as suggested by the celebrated work of Hans Lewy, Nirenberg, and Treves. We have recently discovered a new face of CR Geometry which regards CR manifolds as certain Dynamical Systems, and vice versa. Geometric properties of CR manifolds are in one-to-one correspondence with that of the associated dynamical systems. This technique has enabled us recently to solve a number of long-standing problems in CR Geometry. It also has promising applications for Dynamical Systems. In this talk, we will outline this technique, and describe its recent applications to Complex Analysis and Dynamics. In particular, we will discuss here an approach for studying Painleve Differential Equations.

1:00 pm in 345 Altgeld Hall,Tuesday, October 27, 2015

#### Ramsey classes with algebraic closure and forbidden homomorphisms

###### Jan Hubicka (University of Calgary)

Abstract: Class K of finite structures is Ramsey if for every choice of A and B in K there exists C in K such that for every coloring of its substructures isomorphic to A with 2 colors there exists an isomorphic copy of B in C where all copies of A are monochromatic. In 2005, Kerchris, Pestov and Todorcevic found an important link between Ramsey structures and topological dynamics and motivated search for new Ramsey classes. I will discuss a recent extension of Nesetril-Rodl theorem to classes with non-trivial algebraic closures and with forbidden homomorphic images. This framework simplifies many existing proofs of Ramsey property (such as for acyclic graphs, partial orders or metric spaces) and introduces new ones (such as expansions for Sherlin-Shelah-Shi classes).

1:00 pm in At a restaurant TBA,Tuesday, October 27, 2015

#### Dynamics and Cauchy-Riemann Geometry

###### Ilya Kossovskiy (Univ. of Vienna)

Abstract: The seminar will meet jointly with the Geometry, Groups, and Dynamics seminar at 12:00. We will then have lunch at 1:00.

3:00 pm in 241 Altgeld Hall,Tuesday, October 27, 2015

#### Examples of Ramsey lifts

###### Jan Hubička   [email] (University of Calgary)

Abstract: Class $K$ of finite structures is Ramsey if for every choice of $A$ and $B$ in $K$ there exists $C$ in $K$ such that for every coloring of its substructures isomorphic to $A$ with $2$ colors there exists an isomorphic copy of $B$ in $C$ where all copies of $A$ are monochromatic. The notion of Ramsey classes was introduced in 1970s as a structural generalization of Ramsey's theorem. It follows directly from Ramsey's theorem that the class of all finite linear order is a Ramsey class. It is easy to see that the class of all finite graphs is not Ramsey. Nešetřil and Rődl however shown that the class of all finite graphs can be turned to Ramsey by fixing arbitrary linear order on vertices. Such enriched classes are called Ramsey lifts. I will discuss several recent examples of classes with non-trivial Ramsey lifts and show additional properties (such as the ordering property). The talk is closely related to the talk at logic seminar, but I will provide all necessary definitions to make it independent.

3:00 pm in 243 Altgeld Hall,Tuesday, October 27, 2015

#### Overview of the algebra of hypermatrices and its applications

###### Edinah Gnang (Purdue)

Abstract: In this talk we will present an overview of the hypermatrix generalization of the algebra of matrices proposed in the 90s by D. Mesner and P. Bhattacharya. We will discuss how the algebra naturally extends to hypermatrices important matrix notions including the notion of Unitarity, the notion of matrix inverse, Parseval's identity, the Rayleigh quotient, notions of Discrete Fourier Transforms, the Cayley–Hamilton theorem, the spectral decomposition and various combinatorial interpretation of matrices. Finally if time permits we will discuss applications and some related open problems. No prior knowledge of hypermatrices is assumed for this talk.

4:00 pm in 245 Altgeld Hall,Tuesday, October 27, 2015