I am handing off GAUSS to someone else

picture of craig in the snow saying brrr

GAUSS will no longer be run by Keshav! Thank goodness! Please check with Chris St Clair and Tristan Wells-Filbert.

Thank you to everyone who even thought once about attending, especially to those who never did.

Thank you to Craig who has helped with more than just getting a zoom cart and even hosting sometimes. Craig is a smart mathematician who has been known to feel cold when it snows outside. Warm up, Craig!

GAUSS = Graduate And Undergraduate Student Seminar

Accessible (undergraduate-level) math talks given every week. No solicitors.
~~Please fill out this form to be put on the mailing list or if you want to present, or you can email me directly for details.~~
Both undergraduates and graduates are welcome to talk!

~~Attend from the convenience of your own home: https://msu.zoom.us/j/99892700137.~~

Spring 2022

The GAUSS seminar for spring 2022 will meet in C304 Wells Hall on Tuesdays at 4:00pm (Michigan time).
Funding for milk and cookies provided by the MSU Math department. What were they thinking!
There is also an online option: https://msu.zoom.us/j/99892700137.

It is still run by Keshav! But why!

Date	Speaker	Title	Description
May 3	Keshav!	Hang out and Learn Origami (not a talk)	Come and take a break from finals to hang out with me and learn the only bit of origami that I know (Sonobe units)! I will bring the paper! I will teach you how! I will take your work when you're done! --What? Yes, I need your help to make some shapes to use for the activity I'm helping to run in the upcoming Girls Math and Science Day. (https://midmichigan.wixsite.com/gwis/girlsmathscienceday) But the knowledge you can keep! Food present as usual.
Apr 26	Tristan Wells	Zero-Knowledge Proofs: A Demonstration	First introduced by Goldwasser, Micali, and Rackoff in 1985, zero-knowledge proofs are an interactive (usually) way of proving a claim is true without revealing the contents of the claim. Their paper and another paper by Babai and Moran were enough to achieve the Godel prize in 1993. I will explain the basics according to my own expository understanding and demonstrate a zero-knowledge proof in one simple case. I will then discuss some of the consequences and merits zero-knowledge proofs afford, including uses in cryptography, like cryptocurrencies.
Mar 29	Alexander Sietsema	A stochastic subtraction game, and how to win some money at the bar	Subtraction games, and Nim-like games in general, have long been fundamental examples in the field of combinatorial game theory. In this talk, we will demonstrate and explain the basics of this class of games, introduce a new stochastic variant, and prove two basic theorems about move selection.
Mar 22	Adrian Self	Cracking a Random Number Generator	A pseudorandom number generator is an algorithm to produce random-seeming numbers. More precisely, it can deterministically produce output indistinguishable from a truly random process. For cryptographic usage, it is important that the output is not predictable, even after observing previous outputs. While Bernard Widynski’s “Middle-Square Weyl Sequence PRNG” claims this property, mathematical analysis can be applied using linear congruences to solve for the internal state and predict all future outputs of the random number generator. To demonstrate this, a lottery is simulated, and after a few rounds, we can predict the winning lottery numbers for the rest of time.
Mar 15	Rithwik Vidyarthi	How Topology governs Analysis	Note! Different Time: 3:30-4:30pm Topology deals with shapes and analysis deals with things like calculus. I am going to demonstrate how closely these areas are realted by using the example of R^2 and the punctured plane. At the end of the talk you should be able to distinguish these two spaces using the idea of deforming loops. And how the set of loops determines which vector fields are conservative. You just need to have a working knowledge of calculus to understand most of the talk.
Feb 22	Christopher St Clair	Georg Cantor and Why We Can't Have Nice Things	In this talk we'll explore a few useful counterexamples and constructions to have in our back pocket - most of which are directly or indirectly because of Georg Cantor. These examples are weird now and were weird then so we'll have occasional highlights of Georg's experience along the way. Expect to see a few nuggets of strange math and a bit of strange biography.

Spring 2021

The GAUSS seminar for spring 2021 will be on Fridays at 3:00pm (Michigan time).
It is still run by me! Keshav! How nice!

Date	Speaker	Title	Description
Apr 16	Paula Mercurio	An Introduction to Network Embedding for Data Clustering	I will introduce some of the basic ideas behind network embedding, and show how a complicated or high-dimensional graph can be represented as a collection of points in a lower-dimensional vector space. This will be an expository talk focusing on random walk-based methods, and how these methods are related to certain matrix-based methods and diffusion maps. Throughout the talk, I'll show how these techniques are useful for machine learning tasks like social network analysis and image recognition.
Apr 9	Nick Krupansky	Home Economics 400: Basic financial concepts for entering the working world.	While we have undoubtedly mastered quantitative problem solving, in the coming months many of us will deal with some very common and personal quantitative decisions that we haven't encountered before: retirement benefits. The sooner you have a basic grasp of what benefits are available to you and their impact, the sooner you can make informed decisions and potential compare employment opportunities. As potential new employees, learn the basics of common retirement offerings for US employment and associated tax implications from a student with first-hand experience.
Mar 26	Joe Melby	The Figure Eight Knot (The Friendliest Knot)	Even on its laziest days, the figure-eight knot keeps climbers from falling and a boat's sails in place better than the measly trefoil overhand knot (totally inferior knot). Does the figure-eight save lives? Many would say so. We will discuss the topology and geometry of this life-saving knot, which is the unique 4-crossing and the simplest hyperbolic knot. Our friend the figure-eight knot will guide us as we introduce some important classical concepts and techniques in the fields of knot theory and low-dimensional topology. This is a BYOR (Bring Your Own Rope) event due to COVID-19.
Mar 12	Jamie Schmidt & Alex Sietsema	Pattern Avoidance in Cyclic Permutations	Pattern avoidance in permutations is a well-studied field of enumerative combinatorics. We will discuss the classical version for linear permutations and then introduce a recent variant for cyclic permutations. Finally, we will present our new results counting cyclic avoidance sets for pairs of length 4 patterns and give examples of how those results arise from counting arguments, including a proof for a cyclic variant of the Erdős-Szekeres Therorem.
Mar 5	Chloe Lewis	Taking Topology to the Supreme Court – An Introduction to the Mathematics of Gerrymandering	This year, elected officials in state governments across the country will use the results of the 2020 Census to choose their voters, rather than giving voters the chance to choose them, by drawing unfair Congressional district maps in a process known as gerrymandering. In this talk we’ll look at some mathematical methods of quantifying the partisan gerrymander and discuss the role of the U.S. Supreme Court in informing such methods. Some links from Chloe's talk: SCOTUS opinion - Rucho v. Common Cause Stephanopoulos & McGhee’s law paper Bernstein & Duchin - A Formula Goes to Court Duchin, Needham, Weighill - Persistent homology of maps MGGG Redistricting Lab The preril and promise of redistricting reform in hr1

Fall 2020

The GAUSS seminar for fall 2020 is every Thursday at 4-5pm (Michigan time).
It was started (at MSU) this term and is run by me! Keshav! What a great idea!

Date	Speaker	Title	Description
Dec 10	Abhishek Mallick	Exotica	The geometric structure of the 4-dimensional Euclidean space admits a unique property that is oddly absent from Euclidean space of any other dimensions. In this talk we will have an accessible overview of smooth manifold topology and discuss what is so exoctic about R^4.
Dec 3	Joseph Melby	Exploring Some Interesting 3-manifolds	We will try to visualize and explore candidates for Flatland and Spaceland as well as how they fit together. Then we will board a simulated spaceship together and fly through some of the Spaceland candidates using Jeff Weeks' "Curved Spaces" flight simulator. I promise there will be no subtextual commentary on hierarchy in the culture of Victorian England.
Nov 26	TBA	(Thanksgiving)
Nov 19	Christopher Potvin	Understanding (some) one word proofs	I have often been vexed by textbooks or professors offering one word proofs to quickly justify concepts that do not come so lazily to me. (That's a pangram!) The purpose of this talk will be to shed some light on some of these one word proofs, by giving an introduction to categories. This talk will be accessible to anyone who has ever been similarly frustrated (so all of us), as my examples include things such as the integers, partially ordered sets, and matrices. On the other hand, as a warning, if you can define a natural transformation without looking it up, then this talk will probably be boring for you.
Nov 12	Michalis Paparizos	An introduction to the weight theory and a counterexample to Hytonen's-off testing constant in higher dimensions	The talk starts an introduction to weights and some history in the one and two weight theory and Calderon-Zygmund operators. There is also an introduction to T1 and Tb Theorems and I present a recent result of mine together with Grigoriadis, Sawyer, Shen and Uriarte-Tuero about the two-weight local Tb theorem for fractional singular integral operators.
Nov 5	Noah Ankney	RKHS Structures for von Neumann Algebras	First, I will introduce Hilbert spaces, reproducing kernel Hilbert spaces, and von Neumann algebras. Then, I will show how one may construct a sequence of RKHS's associated to a finite-dimensional von Neumann algebra, which serves as a complete algebraic invariant. Finally, I will describe an RKHS structure which recovers whether or not an arbitrary von Neumann algebra has property Gamma.
Oct 29	Arman Tavakoli	Introduction to Random Projections	I will discuss random projections as a method for dimension reduction, and review one of the main theorems in this topic which is the Johnson-Lindenstrauss lemma. I will explain the lemma and some of the ideas in its proof.
Oct 22	Rachel Domagalski	Inferring relationships through graph theory and social network analysis	Bipartite graphs can be used to capture social networks through event participation. By letting one set of vertices be participants and the other set be events, each edge represents an individual participating in an event. These bipartite graphs can be projected into a weighted graph by multiplying the bipartite adjacency matrix by its transpose. In the projection, an edge between two individuals represents the number of times they participated in the same event. We can now ask, how many times do two people have to participate in events together before we can assume they have some sort of relationship? We will discuss ways to decide if an edge weight is strong enough and deduce friendship ties.
Oct 15	Joshua Ruiter	An algebraic approach to musical scales	This talk is motivated by applications to music theory, especially the construction of musical scales. We'll describe how to think of "good" scales as a subgroups of S^1, then dip our toes into the theory of continued fractions to understand why some "good" scales are "better" than others. In particular, we can get a satisfying mathematical reason for the ubiquity of 12-tone equal temperament scale system.
Oct 8	Craig Gross	Transform your life (fast!) with the Fast Fourier Transform	This will be an expository talk, where we'll begin by introducing Fourier series for periodic functions. After an effusive discussion of their nice properties, we'll move to computer-land and talk about how to approximate coefficients of Fourier series "digitally". This will bring us around to what Gilbert Strang described as "the most important numerical algorithm of our lifetime": the Fast Fourier Transform. We'll talk about how it works and just how fast it really is.