## General Seminar

- English
- Türkçe

This page contains links and recordings for the General Seminar which usually takes place on Thursday, 15:40.

#### Hybrid (Zoom+face-to-face)-Seminars (Fall 2021)

**23.12.2021, Speaker: M. Yasir Kızmaz (METU),***On The Number of Topologies On A Finite Set*We denote the number of distinct topologies which can be defined on a set X with n elements by T(n). Similarly, T_0(n) denotes the number of distinct T_0 topologies on the set X. In this talk, we give the proof of the fact that T(p^k) = k+1 (mod p) and discuss some similar results.*Abstract:**Link: Zoom recording***16.12.2021, Speaker: Bayram Tekin (METU)****, Black Hole Horizons***Abstract:*Black holes emerged as abstract solutions to vacuum Einstein equations. About 100 years of their emergence in theory, their collision was detected experimentally. Since then, there have been many observations of merger of black holes; and there was even a picture of the environment of a supermassive black hole that is as massive as 6.5 Billion suns. I will talk about the Event Horizon of stationary black holes and the Apparent Horizon of dynamical black holes.*Link:*Zoom recording**02.12.2021, Speaker: Özgür Kişisel (METU),***The Expected Depth of Random Real Algebraic Plane Curves**Abstract:*In this talk, I will describe recent joint work with T.Bayraktar on certain questions about random real algebraic plane curves. More precisely, we obtain a Kac-Rice formula for the expected depth of a point with respect to a random algebraic curve of a given degree in the real projective plane. The expected depth is defined as the number of ovals of the curve winding around that point. For certain probability measures on the set of polynomials in question, one can calculate a precise formula for the expected depth in terms of degree.*Link:*Zoom recording, Passcode: