AMS Student Chapter Seminar: Difference between revisions

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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, 3:20 PM – 3:50 PM
* '''When:''' Thursdays 4:00-4:30pm
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]
* '''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 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.


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


== Fall 2018 ==
== 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]]


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.


=== September 26, Vladimir Sotirov ===
Very approachable if you know what a group is but does require tons of ping pong experience.
 
|-
Title: Geometric Algebra
| bgcolor="#D0D0D0" |October 3
 
| bgcolor="#A6B658" |Karthik Ravishankar
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.
| bgcolor="#BCD2EE" |Incompleteness for the working mathematician
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space.
| 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!
 
|-
=== October 3, Juliette Bruce ===
| bgcolor="#D0D0D0" |October 10
 
| bgcolor="#A6B658" |Elizabeth Hankins
Title: Kissing Conics
| bgcolor="#BCD2EE" |Mathematical Origami and Flat-Foldability
 
| 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: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.
|-
 
| bgcolor="#D0D0D0" |October 17
=== October 10, Kurt Ehlert ===
| bgcolor="#A6B658" |CANCELLED
 
| bgcolor="#BCD2EE" |NONE
Title: How to bet when gambling
| bgcolor="#BCD2EE" |NONE
 
|-
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.
| bgcolor="#D0D0D0" |October 24
 
| bgcolor="#A6B658" |CANCELLED
=== October 17, Bryan Oakley ===
| bgcolor="#BCD2EE" |NONE
 
| bgcolor="#BCD2EE" |NONE
Title: Mixing rates
|-
 
| bgcolor="#D0D0D0" |October 31
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.
| bgcolor="#A6B658" |Jacob Wood
 
| bgcolor="#BCD2EE" |What is the length of a <s>potato</s> pumpkin?
=== October 24, Micky Soule Steinberg ===
| 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.
 
|-
Title: What does a group look like?
| bgcolor="#D0D0D0" |November 7
 
| bgcolor="#A6B658" |CANCELLED: DISTINGUISHED LECTURE
Abstract: In geometric group theory, we often try to understand groups by understanding the metric spaces on which the groups act geometrically. For example, Z^2 acts on R^2 in a nice way, so we can think of the group Z^2 instead as the metric space R^2.
| bgcolor="#BCD2EE" |NONE
 
| bgcolor="#BCD2EE" |NONE
We will try to find (and draw) such a metric space for the solvable Baumslag-Solitar groups BS(1,n). Then we will briefly discuss what this geometric picture tells us about the groups.
|-
 
| bgcolor="#D0D0D0" |November 14
=== October 31, Sun Woo Park ===
| bgcolor="#A6B658" |Sapir Ben-Shahar
 
| bgcolor="#BCD2EE" |Hexaflexagons
Title: Induction-Restriction Operators
| 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.
 
|-
Abstract: Given a "nice enough" finite descending sequence of groups <math> G_n \supsetneq G_{n-1} \supsetneq \cdots \supsetneq G_1 \supsetneq \{e\} </math>, we can play around with the relations between induced and restricted representations. We will construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is a commutative polynomial ring over <math> \mathbb{Z} </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 </math>. (Apart from the talk, I'll also prepare some treats in celebration of Halloween.)
| bgcolor="#D0D0D0" |November 21
 
| bgcolor="#A6B658" |Andrew Krenz
=== November 7, Polly Yu ===
| bgcolor="#BCD2EE" |All concepts are database queries
 
| 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.
Title: Positive solutions to polynomial systems using a (mostly linear) algorithm
|-
 
| bgcolor="#D0D0D0" |November 28
Abstract: "Wait, did I read the title correctly? Solving non-linear systems using linear methods?” Yes you did. I will present a linear feasibility problem for your favourite polynomial system; if the algorithm returns an answer, you’ve gotten yourself a positive solution to your system, and more than that, the solution set admits a monomial parametrization.
| bgcolor="#A6B658" |THANKSGIVING
 
| bgcolor="#BCD2EE" |NONE
=== November 14, Soumya Sankar ===
| bgcolor="#BCD2EE" |NONE
 
|-
Title: The worlds of math and dance
| bgcolor="#D0D0D0" |December 5
 
| bgcolor="#A6B658" |Caroline Nunn
Abstract: Are math and dance related? Can we use one to motivate problems in the other? Should we all learn how to dance? I will answer these questions and then we will have some fun with counting problems motivated by dance.
| bgcolor="#BCD2EE" |Watch Caroline eat a donut: an introduction to Morse theory
 
| bgcolor="#BCD2EE" |Morse theory has been described as "one of the deepest applications of differential geometry to topology." However, the concepts involved in Morse theory are so simple that you can learn them just by watching me eat a donut (and subsequently watching me give a 20 minute talk explaining Morse theory.) No background is needed beyond calc 3 and a passing familiarity with donuts.
=== November 28, Niudun Wang ===
|}
 
</center>
Title: Continued fraction's bizarre adventure
 
Abstract: When using fractions to approximate a real number, continued fraction is known to be one of the fastest ways. For instance, 3 is close to pi (somehow), 22/7 was the best estimate for centuries, 333/106 is better than 3.1415 and so on. Beyond this, I am going to show how continued fraction can also help us with finding the unit group of some real quadratic fields. In particular, how to solve the notorious Pell's equation.
 
=== December 5, Patrick Nicodemus ===
 
Title: Applications of Algorithmic Randomness and Complexity
 
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.
 
=== December 12, Wanlin Li ===
 
Title: Torsors
 
Abstract: I will talk about the notion of torsor based on John Baez's article 'Torsors made easy' and I will give a lot of examples. This will be a short and light talk to end the semester.
 
== Spring 2019 ==
 
 
=== February 6, TBD ===
 
Title: TBD
 
Abstract: TBD
 
=== February 13, TBD ===
 
Title: TBD
 
Abstract: TBD
 
=== February 20, TBD ===
 
Title: TBD
 
Abstract: TBD
 
=== February 27, TBD ===
 
Title: TBD
 
Abstract: TBD
 
=== March 6, TBD ===
 
Title: TBD
 
Abstract: TBD
 
=== March 13, TBD ===
 
Title: TBD
 
Abstract: TBD
 
=== March 27 (Prospective Student Visit Day), Multiple Speakers ===
 
Speaker: TBD
 
Title: TBD
 
Abstract: TBD
 
=== April 3, TBD ===
 
Title: TBD
 
Abstract: TBD
 
=== April 10, TBD ===
 
Title: TBD
 
Abstract: TBD
 
=== April 17, TBD ===
 
Title: TBD
 
Abstract: TBD
 
=== April 24, TBD ===
 
Title: TBD
 
Abstract: TBD

Latest revision as of 19:14, 2 December 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 Watch Caroline eat a donut: an introduction to Morse theory Morse theory has been described as "one of the deepest applications of differential geometry to topology." However, the concepts involved in Morse theory are so simple that you can learn them just by watching me eat a donut (and subsequently watching me give a 20 minute talk explaining Morse theory.) No background is needed beyond calc 3 and a passing familiarity with donuts.
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