##### Seminars and Colloquia

**Seminars are held in room S-104. (Click talk titles to see available abstracts.) **

- Fri, June 28, 2019 at 15:30--16:30.
**Keisuke Arai**(Tokyo Denki University)

Non-existence of rational points on Shimura curves and its function field analogueThe moduli space of QM-abelian surfaces (i.e., two-dimensional abelian varieties with an action of a maximal order of a quaternion algebra) is called a Shimura curve. I will talk about non-existence of rational points on Shimura curves as well as Hasse principle violations. The moduli space of D-elliptic sheaves (or Drinfeld-Stuhler modules) is a function field analogue of a Shimura curve. I will also talk about analogous results for function fields. The latter is a joint work with Satoshi Kondo and Mihran Papikian.

- Fri, Dec 26 at 14:40.
**Süleyman Ulusoy**(Zirve University)

Localization, smoothness and convergence to equilibrium for a thin film equationWe investigate the long-time behavior of weak solutions to the thin-film type equation*vt = (x ‧ v – v ‧ vxxx)x*,which arises in the Hele-Shaw problem. We estimate that the rate of convergence of solutions to the Smyth-Hill equilibrium solution, which has the form*1⁄24 (C2 – x2)2+*, in the norm*‖ f ‖2m,1 = ∫R (1 + |x|2m) | f(x) |2 dx + ∫R | fx(x) |2 dx*.We obtain exponential convergence in the*‖‧‖m,1*norm for all*m*with*1 ≤ m < 2*thus obtaining rates of convergence in norms measuring both smoothness and localization. The localization is the main novelty, and in fact, we show that there is a close connection between the localization bounds and the smoothness bounds: Convergence of second moments implies convergence in the*H1*Sobolev norm. We then use methods of optimal mass transportation to obtain the convergence of the required moments. We also use such methods to construct an appropriate class of weak solutions for which all of the estimates on which our convergence analysis depends may be rigorously derived. Though our main results on convergence can be stated without reference to optimal mass transportation, essential use of this theory is made throughout our analysis.

The general seminar is Thursdays 13:40-14:40. The special seminar is Tuesdays 13:40-14:40.

The general seminar is Thursdays 13:40-14:40. The special seminar is Tuesdays 13:40-14:40.

- Tuesdays at 13:40.
**Munnever Celik**(METU)

(Special Seminar) Drinfeld's Double and R-Matrices

- Tue, Sept 24 and Oct 1 at 13:40.
**Ozgur Kisisel**(METU)

(Special Seminar) Overview of Quantum Groups and Knots I/II(Two lectures) Review of lectures on quantum groups and knots from last year, as well as overview of remaining results.

- Thu, Sept 26 and Oct 3 at 13:40.
**Ozgur Kisisel**(METU)

(General Seminar) Tropical Geometry I/II(Two lectures) We will give a general overview of tropical geometry: What things are and how they've been used. Also some new work will be outlined. If interest continues further lectures can be given during the special seminar.

- Thu, Oct 10 and 24 at 13:40.
**Salih Durhan**(METU)

(General Seminar)Valued Fields and Tropical Geometry I/II(two lectures)

- Thu, Nov 7 and 14 at 13:40.
**Ibrahim Unal**(METU)

(General Seminar) φ-free Submanifolds and Convexity in Calibrated ManifoldsF. R. Harvey and H. B. Lawson, Jr. canonically generalized the classical plurisubharmonic functions and convexity in complex geometry to all calibrated manifolds, and called them φ-plurisubharmonic functions and φ-convexity on a calibrated manifold*(X,φ)*. One of the techniques to construct enormous families of strictly φ-convex domains with different topological types is using φ-free submanifolds, analogues of totally real submanifolds. In this talk, I will speak about the topology of φ-free submanifolds for well-known calibrations in Quaternion-Kähler,*G2*and*Spin(7)*manifolds and explain some recent results about φ-free embeddings, which use*h*-principle.

- Thu, Nov 28 and Dec 5 and Dec 12 at 13:40.
**Anar Dosi**(METU)

(General Seminar) Noncommutative Algebraic Geometry

- Thu, Dec 19 and Jan 2 at 13:40.
**Benjamin Walter**(METU)

(General Seminar) Chromatic Numbers, Homotopy, and Calculus(Two lectures)