**Problem of the Week**

**Math Club**

**BUGCAT 2018**

**DST and GT Day**

**Number Theory Conf.**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

seminars:topsem

We meet **Thursdays** at **2:50–3:50 pm** in **WH-100E** followed by refreshments served from 4:00–4:25 pm in WH-102. This semester's organizer is Jonathan Williams.

Some seminar speakers will also give a colloquium talk at **4:30 pm** on the same day as the seminar talk. This seminar is partly funded as one of Dean's Speaker Series in Harpur College (College of Arts and Sciences) at Binghamton University.

The seminar has an announcement mailing list open to all. There is also a Google calendar with the seminar schedule (also in iCal).

**February 21**

Speaker:**Ben Dozier**(Stony Brook)

Title:**Equidistribution of billiard trajectories and translation surfaces***Abstract:*Consider a billiard ball bouncing around on a polygonal table. This dynamical system is surprisingly complex. When the angles of the table are rational, the billiard table can be “unfolded” to get a closed surface with a natural flat geometry. This is an example of a translation surface. Billiard trajectories on the original table unfold to straight lines on the translation surface. Translation surfaces form a moduli space (which is a bundle over $M_g$, the moduli space of genus g Riemann surfaces), and this space comes equipped with a natural action by $SL_2(\mathbb R)$. Through a technique of “renormalization”, questions about the dynamics on a fixed surface can be translated into questions about the dynamics associated with this $SL_2(\mathbb R)$ action. The $SL_2(\mathbb R)$ action is very rich, and analogies with homogeneous dynamics can be leveraged.

**February 28**

Speaker:**Cary Malkiewich**(Binghamton)

Title:**Parametrized spectra and fixed-point theory***Abstract:*In 1980, Dold and Puppe presented a revisionist proof of the Lefschetz fixed point theorem. The main idea is that the Lefschetz number L(f) is secretly more than a number, it's actually a map of spectra. Their ideas can be generalized to the Reidemeister trace R(f), or to families of fixed-point problems, but these generalizations require us to work with parametrized spectra, in other words spectra that vary over a fixed base B. I'll talk about what these words mean, and some cool things we can prove once we have them in our toolbox.

**March 7**

Speaker:**Yash Lodha**(Ecole Polytechnique federale de Lausanne)

Title:**Finitely generated simple left orderable groups, commutator width and orderable monsters***Abstract:*In 1980 Rhemtulla asked whether there exist finitely generated simple left orderable groups. In joint work with Hyde, we construct continuum many such examples, thereby resolving this question. In recent joint work with Hyde, Navas, and Rivas, we demonstrate that among these examples are also so called ``left orderable monsters”. This means that all their actions on the real line are of a certain desirable dynamical type. This resolves a question from Navas's 2018 ICM proceedings article concerning the existence of such groups.

**March 14**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**March 21 - No seminar (Spring break)**

**March 28**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**April 4 - Peter Hilton Memorial Lecture**

Special time and place: LH 9, 3pm

Speaker:**Shmuel Weinberger**(University of Chicago)

Title:**How hard is algebraic topology? Between the constructive and the non.***Abstract:*In algebraic topology one studies geometric problems and problems of constructing and deforming highly nonlinear functions by means of algebra. If one knows that two maps are homotopic (i.e. can be deformed to one another) because a certain calculation says they both lie in the trivial group, then what has one learned? (A striking example of this is Smale's turning the sphere inside out, which now can be seen after much highly nontrivial effort, on youtube.) The question I shall discuss is how hard is it to understand what the algebraic topologists tell us.

**April 11**

Speaker:**Matt Zaremsky**(Albany)

Title:**TBA***Abstract:*TBA

**April 18**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**April 25**

Speaker:**Hyunki Min**(Georgia Tech)

Title:**TBA***Abstract:*TBA

**May 2**

Speaker:**Kate Ponto**(Institution)

Title:**TBA***Abstract:*TBA

**May 9**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

seminars/topsem.txt · Last modified: 2019/02/18 08:51 by jwilliams

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