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The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.
The AMS Student Chapter Seminar (aka Donut Seminar) is an informal, graduate student seminar on a wide range of mathematical topics. The goal of the seminar is to promote community building and give graduate students an opportunity to communicate fun, accessible math to their peers in a stress-free (but not sugar-free) environment. Pastries (usually donuts) will be provided.


* '''When:''' Wednesdays, 3:00 PM – 3:30 PM
* '''When:''' Thursdays 4:00-4:30pm
* '''Where:''' Van Vleck, 9th floor lounge
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)
* '''Organizers:''' Laura Cladek, Ryan Julian, Xianghong Chen, Daniel Hast
* '''Organizers:''' Ivan Aidun, Kaiyi Huang, Ethan Schondorf


Everyone is welcome to give a talk. To sign up, please contact the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 25 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.


==Spring 2015==
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].


===January 28, Moisés Herradón===
== Fall 2024 ==
<center>
{| cellspacing="5" cellpadding="14" border="0" style="color:black; font-size:120%"
! align="center" width="200" bgcolor="#D0D0D0" |'''Date'''
! align="center" width="200" bgcolor="#A6B658" |'''Speaker'''
! align="center" width="300" bgcolor="#BCD2EE" |'''Title'''
! align="center" width="400" bgcolor="#BCD2EE" |'''Abstract'''
|-
| bgcolor="#D0D0D0" |September 12
| bgcolor="#A6B658" |Ari Davidovsky
| bgcolor="#BCD2EE" |95% of people can't solve this!
| bgcolor="#BCD2EE" | [[File:Image.png|360px]]


Title: Winning games and taking names
We will attempt to answer this question and along the way explore how algebra and geometry work together to solve problems in number theory.
|-
| bgcolor="#D0D0D0" |September 19
| bgcolor="#A6B658" |CANCELLED
| bgcolor="#BCD2EE" |NONE
| bgcolor="#BCD2EE" |NONE
|-
| bgcolor="#D0D0D0" |September 26
| bgcolor="#A6B658" |Mateo Morales
| bgcolor="#BCD2EE" |Officially petitioning the department to acquire a ping pong table.
| bgcolor="#BCD2EE" |Ever want to prove something is a free group of rank 2? Me too. One way to do this is to use a ping pong argument of how a group generated by two elements acts on a set.
I will illustrate the ping pong argument using an example of matrices, explain how it works, and explain why, kinda.


Abstract:  So let’s say we’re already amazing at playing one game (any game!) at a time and we now we need to play several games at once, to keep it challenging. We will see that doing this results in us being able to define an addition on the collection of all games, and that it actually turns this collection into a Group. I will talk about some of the wonders that lie within the group. Maybe lions? Maybe a field containing both the real numbers and the ordinals? For sure it has to be one of these two!
Very approachable if you know what a group is but does require tons of ping pong experience.
 
|-
===February 11, Becky Eastham===
| bgcolor="#D0D0D0" |October 3
 
| bgcolor="#A6B658" |Karthik Ravishankar
Title: A generalization of van der Waerden numbers: (a, b) triples and (a_1, a_2, ..., a_n) (n + 1)-tuples
| bgcolor="#BCD2EE" |Incompleteness for the working mathematician
 
| bgcolor="#BCD2EE" |In this talk we'll take a look at Gödels famous incompleteness theorems and look at some of its immediate as well as interesting consequences. No background in logic is necessary!
Abstract: Van der Waerden defined w(k; r) to be the least positive integer such that for every r-coloring of the integers from 1 to w(k; r), there is a monochromatic arithmetic progression of length k.  He proved that w(k; r) exists for all positive k, r.  I will discuss the case where r = 2.  These numbers are notoriously hard to calculate: the first 6 of these are 1, 3, 9, 35, 178, and 1132, but no others are known.  I will discuss properties of a generalization of these numbers, (a_1, a_2, ..., a_n) (n + 1)-tuples, which are sets of the form {d, a_1x + d, a_2x + 2d, ..., a_nx + nd}, for d, x positive natural numbers.
|-
 
| bgcolor="#D0D0D0" |October 10
===February 18, Solly Parenti===
| bgcolor="#A6B658" |Elizabeth Hankins
 
| bgcolor="#BCD2EE" |Mathematical Origami and Flat-Foldability
Title: Chebyshev's Bias
| bgcolor="#BCD2EE" |If you've ever unfolded a piece of origami, you might have noticed complicated symmetries in the pattern of creases left behind. What patterns of lines can and cannot be folded into origami? And why is it sometimes hard to determine?
 
|-
Abstract: Euclid told us that there are infinitely many primes.  Dirichlet answered the question of how primes are distributed among residue classes.  This talk addresses the question of "Ya, but really, how are the primes distributed among residue classes?" Chebyshev noted in 1853 that there seems to be more primes congruent to 3 mod 4 than their are primes congruent to 1 mod 4.  It turns out, he was right, wrong, and everything in between. No analytic number theory is presumed for this talk, as none is known by the speaker.
| bgcolor="#D0D0D0" |October 17
 
| bgcolor="#A6B658" |CANCELLED
===February 25, David Bruce===
| bgcolor="#BCD2EE" |NONE
 
| bgcolor="#BCD2EE" |NONE
Title: Mean, Median, and Mode - Well Actually Just Median
|-
 
| bgcolor="#D0D0D0" |October 24
Abstract: Given a finite set of numbers there are many different ways to measure the center of the set. Three of the more common measures, familiar to any middle school students, are: mean, median, mode. This talk will focus on the concept of the median, and why in many ways it's sweet. In particular, we will explore how we can extend the notion of a median to higher dimensions, and apply it to create more robust statistics. It will be awesome, and there will be donuts.
| bgcolor="#A6B658" |CANCELLED
 
| bgcolor="#BCD2EE" |NONE
===March 4, Jing Hao===
| bgcolor="#BCD2EE" |NONE
 
|-
Title: Error Correction Codes
| bgcolor="#D0D0D0" |October 31
 
| bgcolor="#A6B658" |Jacob Wood
Abstract: In the modern world, many communication channels are subject to noise, and thus errors happen. To help the codes auto-correct themselves, more bits are added to the codes to make them more different from each other and therefore easier to tell apart. The major object we study is linear codes. They have nice algebraic structure embedded, and we can apply well-known algebraic results to construct 'nice' codes. This talk will touch on the basics of coding theory, and introduce some famous codes in the coding world, including several prize problems yet to be solved!
| bgcolor="#BCD2EE" |What is the length of a <s>potato</s> pumpkin?
 
| bgcolor="#BCD2EE" |How many is a jack-o-lantern? What is the length of a pumpkin? These questions sound like nonsense, but they have perfectly reasonable interpretations with perfectly reasonable answers. On our journey through the haunted house with two rooms, we will encounter some scary characters like differential topology and measure theory. Do not fear; little to no experience in either subject is required.
===March 10 (Tuesday), Nathan Clement===
|-
 
| bgcolor="#D0D0D0" |November 7
''Note: This week's seminar will be on Tuesday at 3:30 instead of the usual time.''
| bgcolor="#A6B658" |CANCELLED: DISTINGUISHED LECTURE
 
| bgcolor="#BCD2EE" |NONE
Title: Two Solutions, not too Technical, to a Problem to which the Answer is Two
| bgcolor="#BCD2EE" |NONE
 
|-
Abstract: A classical problem in Algebraic Geometry is this: Given four pairwise skew lines, how many other lines intersect all of them. I will present some (two) solutions to this problem. One is more classical and ad hoc and the other introduces the Grassmannian variety/manifold and a little intersection theory.
| bgcolor="#D0D0D0" |November 14
 
| bgcolor="#A6B658" |Sapir Ben-Shahar
===March 25, Eric Ramos===
| bgcolor="#BCD2EE" |Hexaflexagons
 
| bgcolor="#BCD2EE" |Come along for some hexaflexafun and discover the mysterious properties of hexaflexagons, the bestagons! Learn how to make and navigate through the folds of your very own paper hexaflexagon. No prior knowledge of hexagons (or hexaflexagons) is assumed.
Title: Braids, Knots and Representations
|-
 
| bgcolor="#D0D0D0" |November 21
Abstract: In the 1920's Artin defined the braid group, B_n, in an attempt to understand knots in a more algebraic setting. A braid is a certain arrangement of strings in three-dimensional space. It is a celebrated theorem of Alexander that every knot is obtainable from a braid by identifying the endpoints of each string. Because of this correspondence, the Jones and Alexander polynomials, two of the most important knot invariants, can be described completely using the braid group. In fact, Jones was able to show that knot invariants can often be realized as characters of special representations of the braid group.
| bgcolor="#A6B658" |Andrew Krenz
 
| bgcolor="#BCD2EE" |All concepts are database queries
The purpose of this talk is to give a very light introduction to braid and knot theory. The majority of the talk will be comprised of drawing pictures, and nothing will be treated rigorously.
| bgcolor="#BCD2EE" |A celebrated result of applied category theory states that the category of small categories is equivalent to the category of database schemas. Therefore, every theorem about small categories can be interpreted as a theorem about databases.  Maybe you've heard someone repeat Mac Lane's famous slogan "all concepts are Kan extensions."  In this talk, I'll give a high-level overview of/introduction to categorical database theory (developed by David Spivak) wherein Kan extensions play the role of regular every day database queries.  No familiarity with categories or databases will be assumed.
 
|-
===April 8, James Waddington===
| bgcolor="#D0D0D0" |November 28
 
| bgcolor="#A6B658" |THANKSGIVING
Title: Goodstein's Theorem
| bgcolor="#BCD2EE" |NONE
 
| bgcolor="#BCD2EE" |NONE
Abstract: One of the most important results in the development of mathematics are
|-
Gödel's Incompleteness theorems. The first incompleteness theorem shows that no
| bgcolor="#D0D0D0" |December 5
list of axioms one could provide could extend number theory to a complete and
| bgcolor="#A6B658" |Caroline Nunn
consistent theory. The second showed that one such statement was no
| bgcolor="#BCD2EE" |TBA
axiomatization of number theory could be used to prove its own consistency.
| bgcolor="#BCD2EE" |T
Needless to say this was not viewed as a very natural independent statement
|}
from arithmetic.
</center>
 
Examples of non-metamathematical results that were independent of PA, but true
of second order number theory, were not discovered until much later. Within a
short time of each three such statements that were more "natural" were
discovered. The Paris–Harrington Theorem, which was about a statement in Ramsey
theory, the Kirby–Paris theorem, which showed the independence of Goodstein's
theorem from Peano Arithmetic and the Kruskal's tree theorem, a statement about
finite trees.
 
In this talk I shall discuss Goodstein's theorem which discusses the end
behavior of a certain "Zero player" game about k-nary expansions of numbers.
I will also give some elements of the proof of the Kirby–Paris theorem.
 
===April 22, William Cocke===
 
Title: Finite Groups aren't too Square
 
Abstract: We investigate how many non-p-th powers a group can have for a given prime p.
We will show using some elementary group theory, that if np(G) is the number of non-p-th powers
in a group G, then G has order bounded by np(G)(np(G)+1). Time permitting we will show this bound
is strict and that mentioned results involving more than finite groups.
 
==Fall 2014==
 
===September 25, Vladimir Sotirov===
 
Title: [[Media:Compact-openTalk.pdf|The compact open topology: what is it really?]]
 
Abstract:  The compact-open topology on the space C(X,Y) of continuous functions from X to Y is mysteriously generated by declaring that for each compact subset K of X and each open subset V of Y, the continous functions f: X->Y conducting K inside V constitute an open set. In this talk, I will explain the universal property that uniquely determines the compact-open topology, and sketch a pretty constellation of little-known but elementary facts from domain theory that dispell the mystery of the compact-open topology's definition.
 
===October 8, David Bruce===
 
Title: Hex on the Beach
 
Abstract: The game of Hex is a two player game played on a hexagonal grid attributed in part to John Nash. (This is the game he is playing in /A Beautiful Mind./) Despite being relatively easy to pick up, and pretty hard to master, this game has surprising connections to some interesting mathematics. This talk will introduce the game of Hex, and then explore some of these connections. *As it is a lot more fun once you've actually played Hex feel free to join me at 3:00pm on the 9th floor to actually play a few games of Hex!*
 
===October 22, Eva Elduque===
 
Title: The fold and one cut problem
 
Abstract: What shapes can we get by folding flat a piece of paper and making (only) one complete straight cut? The answer is surprising: We can cut out any shape drawn with straight line segments. In the talk, we will discuss the two methods of approaching this problem, focusing on the straight skeleton method, the most intuitive of the two.
 
===November 5, Megan Maguire===
 
Title: Train tracks on surfaces
 
Abstract: What is a train track, mathematically speaking? Are they interesting? Why are they interesting? Come find out!
 
===November 19, Adrian Tovar-Lopez===
 
Title:  Hodgkin and Huxley equations of a single neuron
 
===December 3, Zachary Charles===
 
Abstract: An addition chain is a sequence of numbers starting at one, such that every number is the sum of two previous numbers. What is the shortest chain ending at a number n? While this is already difficult, we will talk about how addition chains answer life's difficult questions, including: How do we compute 2^4? What can the Ancient Egyptians teach us about elliptic curve cryptography? What about subtraction?

Latest revision as of 18:18, 20 November 2024

The AMS Student Chapter Seminar (aka Donut Seminar) is an informal, graduate student seminar on a wide range of mathematical topics. The goal of the seminar is to promote community building and give graduate students an opportunity to communicate fun, accessible math to their peers in a stress-free (but not sugar-free) environment. Pastries (usually donuts) will be provided.

  • When: Thursdays 4:00-4:30pm
  • Where: Van Vleck, 9th floor lounge (unless otherwise announced)
  • Organizers: Ivan Aidun, Kaiyi Huang, Ethan Schondorf

Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 25 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.

The schedule of talks from past semesters can be found here.

Fall 2024

Date Speaker Title Abstract
September 12 Ari Davidovsky 95% of people can't solve this! Image.png

We will attempt to answer this question and along the way explore how algebra and geometry work together to solve problems in number theory.

September 19 CANCELLED NONE NONE
September 26 Mateo Morales Officially petitioning the department to acquire a ping pong table. Ever want to prove something is a free group of rank 2? Me too. One way to do this is to use a ping pong argument of how a group generated by two elements acts on a set.

I will illustrate the ping pong argument using an example of matrices, explain how it works, and explain why, kinda.

Very approachable if you know what a group is but does require tons of ping pong experience.

October 3 Karthik Ravishankar Incompleteness for the working mathematician In this talk we'll take a look at Gödels famous incompleteness theorems and look at some of its immediate as well as interesting consequences. No background in logic is necessary!
October 10 Elizabeth Hankins Mathematical Origami and Flat-Foldability If you've ever unfolded a piece of origami, you might have noticed complicated symmetries in the pattern of creases left behind. What patterns of lines can and cannot be folded into origami? And why is it sometimes hard to determine?
October 17 CANCELLED NONE NONE
October 24 CANCELLED NONE NONE
October 31 Jacob Wood What is the length of a potato pumpkin? How many is a jack-o-lantern? What is the length of a pumpkin? These questions sound like nonsense, but they have perfectly reasonable interpretations with perfectly reasonable answers. On our journey through the haunted house with two rooms, we will encounter some scary characters like differential topology and measure theory. Do not fear; little to no experience in either subject is required.
November 7 CANCELLED: DISTINGUISHED LECTURE NONE NONE
November 14 Sapir Ben-Shahar Hexaflexagons Come along for some hexaflexafun and discover the mysterious properties of hexaflexagons, the bestagons! Learn how to make and navigate through the folds of your very own paper hexaflexagon. No prior knowledge of hexagons (or hexaflexagons) is assumed.
November 21 Andrew Krenz All concepts are database queries A celebrated result of applied category theory states that the category of small categories is equivalent to the category of database schemas. Therefore, every theorem about small categories can be interpreted as a theorem about databases.  Maybe you've heard someone repeat Mac Lane's famous slogan "all concepts are Kan extensions."  In this talk, I'll give a high-level overview of/introduction to categorical database theory (developed by David Spivak) wherein Kan extensions play the role of regular every day database queries.  No familiarity with categories or databases will be assumed.
November 28 THANKSGIVING NONE NONE
December 5 Caroline Nunn TBA T
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