Short Attention Span Math Seminars

Winter 2019

The Winter 2019 SASMS will be held on Monday, March 11 at 4:00 in MC 5417. If you would like to give a talk, you may do so by clicking "Sign Up" above.

Talks

Time
Speaker
Talk Title
4:00
Jose Luis Avilez
Demystifying myths: Neural networks under the lens of functional analysis
4:30
Zia Allahverdiyev
The Power of Powers
5:00
Zouhaier Ferchiou
Rambling about my favorite degenerate group
5:30
Jerry Guan
The Snake Lemma
6:00
Food
DIN 146: Introduction to Human Nutrition
6:30
Stephen Charles Zheng Biao Wen
The Lefschetz Principle
7:00
7:30

Abstracts

Demystifying myths: Neural networks under the lens of functional analysis

In this talk we prove that linear combinations of discriminatory functions are dense in the set of continuous functions. These functions may then form the activation layers in neural networks.

The Power of Powers

Can every large enough integer be represented as a sum of three, four, .... k squares, cubes, .... n? We will be considering all representations of an integer as the sum of powers of distinct positive integers and find the connection between representations containing odd or even number of terms. All of these questions will lead us to "Waring's problem".

Rambling about my favorite degenerate group

We usually assume n > 0 when talking about the dihedral group Dn. What if we don't ?

The Snake Lemma

Used to construct long exact sequences, the snake lemma is an useful tool in homological algebra. This fact holds in any abelian category, and the standard proof by diagram chasing relies on the Freyd-Mitchell theorem to establish this. However, the theorem is very difficult and relies on complicated machinery, so I will present a full proof of the snake lemma using more elementary methods.

DIN 146: Introduction to Human Nutrition

An introductory talk on human nutrition. Attendees will be introduced to core topics in nutrition including fried chicken sandwiches and portobello mushroom sandwiches. Factors that affect nutrition such as pop, chips, and cookies will also be examined. A relaxed social atmosphere may also be covered, time permitting.

The Lefschetz Principle

The Lefschetz Principle gives a way to pass from truth in infinitely many positive characteristics to characteristic 0. Our formalization will come from model theory and we will apply the theorem to questions in algebraic geometry.