# Pure Mathematics Seminar Series

Events

### Agenda

#### Talk 1

Abstract
Luca Demangos would give an overview of the classical theory of elliptic curves and how this plays a fundamental role in the solution of a major open problem, by providing an explicit construction of the abelian closure of every imaginary quadratic number field.

• Tile: Complex Multiplication Theory and Hilbert's 12th problem
• Speaker: Luca Demangos (Department of Mathematical Sciences, XJTLU)
• Time: 1:30-2:30 pm, 15th Jan, Tuesday
• Venue: MB241

#### Talk 2

Abstract
In this talk, Wenyuan Yang will survey some counting results in various classes of non-positively curved group actions. Their study is based on a notion of statistically convex-cocompact actions with a contracting element, which could be thought of as a statistical version of convex-compact Kleinian groups. Moreover, this notion includes relatively hyperbolic groups, CAT(0) groups with rank-1 elements, mapping class groups. With applications towards these groups, Wenyuan Yang will discuss coarse asymptotic formulae of lattice point counting, and of conjugacy classes of elements, and generic free subgroups and statistical hyperbolicity. Part of results are joint with Ilya Gekhtman, and with Suzhen Han.

• Title: The asymptotic geometry of statistically convex-compact actions
• Speaker: Wenyuan Yang (Beijing international center of mathematics, Peking University)
• Biography: Dr Wenyuan Yang got his Phd from Université de Lille 1 in France and is now an associate professor in Peking University. His research focuses on geometric group theory. He was elected to The Thousand Young Talents Program in 2013.
• Time: 1:30-2:30 pm, 17th Jan, Thursday
• Venue: MB241

#### Talk 3

Abstract
For the product $S_1\times S_2$ of any two connected compact hyperbolic surfaces $S_1$ and $S_2$, take advantage of a classification of self-homeomorphisms of $S_1\times S_2$, we give a finite bound $\mathcal{B}$ such that for any self-homeomorphism $f$ of $S_1\times S_2$ and any fixed point class $\F$ of $f$, the index $|\ind(f, \F)|\leq \mathcal{B}$, which is an affirmative answer for a special case of a question asked by Boju Jiang. Moreover, we also give bounds for the Lefschetz number $L(f)$ and the Nielsen number $N(f)$ of the homeomorphism $f$. This is a joint work with ZHAO xuezhi.

• Title: Bounds for fixed points on products of hyperbolic surfaces
• Speaker: Qiang Zhang (School of mathematics, Xi'an Jiaotong University)
• Time: 2:50-3:50 pm, 17th Jan, Thursday
• Venue: MB241