PUBLIC LECTURES

Section: School children

**«On minimizing the energy of macromolecules with an application to protein folding and docking», May 30, 2018**

Instructor: *Alexander Gasnikov (MIPT)*

This lecture is about a real project the ultimate goal of which is developing drugs in the company BIOKAD. The report demonstrates how one can solve problems of protein folding and docking with the help of modern numerical methods of convex optimization.

**«Where and why should I study?»
«If you want to solve problems in game theory this summer, please, come!» ,May 19, 2018**

Instructor: *Dmitry Schwartz (HSE)*

Dr. Schwartz is a graduate of the Moscow State University, PhD in Physics and Mathematics, Associate Professor at the Faculty of Economic Sciences and the Department of Mathematics of the Higher School of Economics. During the meeting, Dr. Schwartz discusses choices of universities and future professions. Schwartz introduces students of Grades 9-10 to the theory of games and proposes interesting problems for solving.

**«Almost planar graphs», May 22-24, 2018**

Instructor: *Alexander Polyansky (MIPT)*

Lectures are devoted to various graphs drawn on the plane. We begin with the classic facts about planar graphs, i.e. graphs drawn on a plane without intersecting edges. In particular, we discuss the Euler formula V-E + F = 2, where V is the number of vertices in the graph, E is the number of edges, F is the number of faces. Then we discuss the method of transferring weights which is used to study graphs drawn on a plane with intersecting edges of certain properties (for example, each edge doesn’t intersects more than once). We discuss how Dilworth’s theorem can be applied in problems related to graphs drawn on the plane.

**«Bijective evidence», May 21, 2018**

Instructor: *Alexander Polyansky (MIPT)*

One of the most ancient mathematical ideas is the idea of bijection. It is possible that it appeared before the concept of numbers. In ancient times, it could be used as follows: the owner has a flock of sheep, each of which lies next to the stone. In the afternoon, the sheep go into the fields, and in the evening, they return. To check that the sheep were not lost (lost, eaten, stolen by a shepherd or by someone else, etc.), the owner could drive the flock to the corral and put each sheep near the stone. If there are unoccupied stones, then one of the sheep is gone, if there are no such stones, then all the sheep are in place. Such an approach to housekeeping does not require knowing how many sheep there are (100 or 1000). It is required only to be able to establish a bijection, and this is very simple. We discuss where this idea is applied in mathematics.