# METU Mathematics Seminars

Fall 2017

Previous Seminars: Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011.

The seminars will be held in Gündüz İkeda Room at 15:40 unless otherwise stated.

October 12

Bilkent University

Straight lines in K3-surfaces

I will discuss a very classical and intuitive problem, namely, counting
straight lines in spatial surfaces. There are infinitely many lines in
planes and quadrics, and there are famous 27 lines in each smooth cubic.
Starting with degree four, a generic surface does not contain a single line;
however, some of them do. I will start with the classical example of quartic
containing 64 lines (Schur, 1882) and move towards very recent results,
including the upper bound of 64 lines for quartics, the classification of
quartics with many lines, bounds for other models of K3-surfaces (sextics in
the 4-space, octics in the 5-space, etc.), and several related statements
(e.g., real lines in real surfaces). Should time permit, fields of
definition of positive characteristic will be considered as well.

The talk should be accessible to graduate and advanced undergraduate and high school students specializing in any area of mathematics.

The talk should be accessible to graduate and advanced undergraduate and high school students specializing in any area of mathematics.

October 19

Bilkent University

Fusion systems and p-local finite groups

If G is a finite group and p a prime dividing the order of G, Sylow's Theorem tells us that G has a p-subgroup of largest possible order, and that such a group is essentially unique. This begins the study of the p-local structure of finite groups: That part of that group visible to a particular prime. These data are organized in a category called a "fusion system."

The p-local study of finite groups has been an area of great interest to group theorists for decades, but more recently connections to algebraic topology have surfaced as well. The Martino-Priddy Conjecture states that two groups have p-equivalent classifying spaces if and only if their fusion systems are isomorphic. In the course of proving this result, it became necessary to think of fusion systems as algebraic objects in their own right, separated from the finite groups in which they originally arose.

Following Puig and Broto-Levi-Oliver, once one has identified the key p-local structures of a finite group, one has introduced a new type of algebraic object, a "p-local finite group." These are group-like algebraic objects that only exist at a particular prime. p-local finite groups can be seen as more general than finite groups, which live in all primes at once. In this talk we will introduce these concepts and give a brief overview of how fusion theory serves as a bridge between finite groups, algebraic topology, and representation theory.

The p-local study of finite groups has been an area of great interest to group theorists for decades, but more recently connections to algebraic topology have surfaced as well. The Martino-Priddy Conjecture states that two groups have p-equivalent classifying spaces if and only if their fusion systems are isomorphic. In the course of proving this result, it became necessary to think of fusion systems as algebraic objects in their own right, separated from the finite groups in which they originally arose.

Following Puig and Broto-Levi-Oliver, once one has identified the key p-local structures of a finite group, one has introduced a new type of algebraic object, a "p-local finite group." These are group-like algebraic objects that only exist at a particular prime. p-local finite groups can be seen as more general than finite groups, which live in all primes at once. In this talk we will introduce these concepts and give a brief overview of how fusion theory serves as a bridge between finite groups, algebraic topology, and representation theory.

October 26

METU

Constructions of Cyclic Subspace Codes and Maximum Rank Distance Codes

This talk is a survey of the recent results on the constructions of cyclic
subspace codes and maximum rank distance codes. Linearized polynomials are the
main tools used to introduce both constructions. This is a joint work with Ferruh Özbudak.

November 2

METU Department of Physics

Mathematics of Gravitational Waves

Direct detection of gravitational waves from merging binary black holes
and binary neutron stars have been recently made. These observations
confirm Einstein's prediction (dating 1916) which says that accelerated
massive objects create propagating ripples in space-time that amounts to
tiny but measurable fluctuations in the metric of space-time. To
interpret the observations, strong field regime of gravity was necessary
to understand.

In this talk I will give a broad summary of the mathematical ideas such as the hyperbolic nature of Einstein's equations and perturbative and exact wave solutions and some related concepts. Gravity waves have just given us another tool to see the past of the universe: for example, neutron star neutron star collision that generated gravity waves also explained the origins of all precious metals silver, gold, platinum and other heavy elements in the universe.

In this talk I will give a broad summary of the mathematical ideas such as the hyperbolic nature of Einstein's equations and perturbative and exact wave solutions and some related concepts. Gravity waves have just given us another tool to see the past of the universe: for example, neutron star neutron star collision that generated gravity waves also explained the origins of all precious metals silver, gold, platinum and other heavy elements in the universe.

November 9

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November 16

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November 23

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November 30

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December 7

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December 14

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December 21

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December 28

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January 4

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