Archive

We invite various University of Texas at Austin faculty members to join us and give lectures about their research, with occasional lectures on other topics. As such, members get the chance to learn about many different subjects in mathematics from a variety of perspectives.

## Spring 2021:

### Dr. John Wright: Interactive Proofs

###

###### May 4th, 2020 at 17:00 CDT

Zoom ID: 945 9458 7391 Password: mathclub

What is a proof? In principle, we think of a proof as a sequence of axioms and inference rules that allow us to derive a mathematical statement. In practice, it's something that typically appears in a textbook or a math journal. In this talk, I'll discuss a different philosophy coming from theoretical computer science, in which a proof can be anything which convinces you. This opens the door to proofs having a variety of different attributes, including being interactive, zero-knowledge, and even quantum.

### Teddy Weisman: Geometry in Minkowski Space

###

###### April 27th, 2020 at 17:00 CDT

Zoom ID: 945 9458 7391 Password: mathclub

In life, we get mileage out of the Euclidean distance formula (d^2 = x^2 + y^2 + z^2): it tells us how to understand aspects of the physical world around us, and it lets us do a lot of cool abstract geometry. But what happens if we change the formula a tiny bit, and make one of the signs negative? It turns out that this modified version of Euclidean length still has real-world significance, and leads to some even cooler abstract geometry. I'll try and explain a bit of both in this talk.

### Dr. Solomon Manukure: Introduction to Nonlinear PDEs and Shallow Water Waves

###

###### April 20th, 2020 at 17:00 CDT

Zoom ID: 945 9458 7391 Password: mathclub

Nonlinear partial differential equations have many applications in mathematical physics. They possess many exact solutions such as solitons, rogue waves, lump and breather solutions, which are ubiquitous in fluid mechanics, gas dynamics, optics, plasma physics, atomic physics and many other areas. In this talk, we will discuss some nonlinear PDEs with applications in shallow water. We will particularly focus on lump and line-rogue wave solutions. We will also give necessary and sufficient conditions for the existence (analyticity and rational localization) of these solutions.

### Dr. Elena Caceres: Tools of Holography

###

###### April 6th, 2020 at 17:00 CDT

Zoom ID: 945 9458 7391 Password: mathclub

Dr. Elena Caceres is an Associate Professor in the Theory Group at the University of Texas at Austin. She is currently researching the relationship between quantum information theory, gravity, and spacetime. She is going to speak about the mathematical tools she uses in her research of the relationship between quantum mechanics and general relativity.

### Luis Torres: Breaking Down 3-Manifolds

###### March 2nd, 2020 at 17:00 CDT

Zoom ID: 945 9458 7391 Password: mathclub

Have you ever wondered about the shape of our universe? Since we live in 3-dimensional space, it’s easy for us to visualize 2-dimensional spaces like a sphere or the surface of a donut. But what are the possible shapes a 3-dimensional space can have? In this talk, I’ll introduce you to 3-dimensional spaces called 3-manifolds, and along the way I’ll show you a few ways you can visualize and construct them via smaller pieces.

### Erin Bevilacqua: Rainbow Numbers and Ramsey Theory

###### March 9th, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

Many interesting results in combinatorics lie in the field of Ramsey Theory. In general, questions in this area ask, "how large do I have to make a structure before I am certain some orderly substructure must exist?" In other words, these are questions that ask about how large objects must be to obtain some degree of order. On the other hand, Anti-Ramsey asks a similar but opposite question: "how much disorder must I apply to a structure of a given size before all substructures are disordered?" In this talk, we will present some interesting results in Ramsey and Anti-Ramsey theory and discuss the concept of rainbow numbers. we will present constructions for the rainbow numbers of both prime and composite n, and a proof that the rainbow number for prime n is exact.

### Dr. Jennifer Austin: I am a Mathematician because...

###### February 23rd, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

Dr. Austin will share her journey to becoming a mathematician, including the challenges and joys along the way. Together we will explore:

(i) What is mathematics?

(ii) What does it mean to think like a mathematician?

Each participant will need an internet-ready device with a webcam, blank paper, and color writing/drawing utensils such as colored pencils, markers, pens, or a tablet with a stylus.

### Casandra Monroe: The Great Beyond

###### February 9th, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

Many talks discuss things that we know in mathematics; this talk will focus on a bunch of things we don't! Expect a smattering of open problems in various fields, from number theory to knot theory. If time permits, I'll try to explain a problem I'm thinking about too!

### Arun Debray: What is a Surface?

###### February 2nd, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

The classification of surfaces for studying surfaces and classifications

The classification of surfaces is a very nice theorem in topology: there is a complete list of examples that fit into a nice pattern, the proof is neither elementary nor too hard, and the answer is useful. One purpose of this talk is to discuss this classification and what exactly is meant by surfaces; another purpose of this talk is to use this to highlight what phenomena can arise when one works on a classification theorem. Topology is not a prerequisite for this talk.

### Rok Gregoric:

###### January 26th, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

### The Sum of Angles of a Triangle, or Curvature and Gauss-Bonnet

We all know what the sum of angles of a triangle is. Or do we? In this talk, we will explore how the answer changes if we try drawing a triangle onto something other than a plane. Using the mathematical notion of curvature, we will explain the beautiful Gauss-Bonnet formula for the sum of angles of a general polygon (with possibly non-straight sides!) on any curved surface.

## Fall 2020:

### Kai Nakamura: The Wild World of 4-Manifolds

An n-dimensional manifold is a space that locally looks like R^n. The study and classification of manifolds is a central topic of study in topology. Manifolds in dimension 4 behave in a completely different way compared to other dimensions, with phenomena that do not occur even in manifolds of dimensions 5 and higher. We will discuss these phenomena and compare them to other dimensions. In particular, if time permits, we'll discuss recent UT phd Lisa Piccirrilo's much acclaimed proof that the Conway knot is not slice.

###### December 1st, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

## Greek Alphabet Crash Course

## November 20th at 15:00 CDT

ZOOM ID: 694 684 6598 Password: mathclub

You’ve almost certainly come across Greek letters before while studying math and physics. But how well do you really know these characters? How

do you pronounce things like Psi and Xi? How does lowercase ξ have anything to do with

capital Ξ? And what the heck is the deal

with ϖ and ϑ? This Friday, 11/20 at

3pm, we’ll go through the

Greek alphabet, from

Alpha to Omega,

and talk

about

how to pronounce and write each character, as well

as common variants you might see in the wild. We’ll also cover a bit of the history and

linguistics behind the Greek alphabet, such as where it originated from, how Phi, Theta,

and Chi were originally pronounced,

and how capital forms became

their lowercase equivalents.

### Jeff Danciger: Inscribing Polyhedra Into a Sphere

Consider a tetrahedron in three-dimensional Euclidean space. There are many different tetrahedra: there are regular tetrahedra, and irregular ones which can look pointy or nearly flat. Some of these tetrahedra are inscribed in the sphere. We say a convex polyhedron is inscribed in the sphere if all of its vertices lie on the unit sphere (and the rest of the polyhedron lies inside the sphere). What other convex polyhedra can be inscribed in the sphere? There are cubes inscribed in the sphere, dodecahedra inscribed in the sphere, and many many other examples. But in fact, some convex polyhedra can not be inscribed in the sphere. How can we tell which ones can be inscribed and which ones can not be? I will share with you a secret formula which answers this question. Though this is a very old question, the solution was discovered only about 25 years ago, using hyperbolic geometry.

###### November 17th, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

For UTMail only:

### Chandrajit Bajaj: Learning to Correct Form and Function with Reinforcement

All biological functions of life are determined by molecular forms. These dynamical events are sensed, directed and modulated by small and large molecules, often in clusters, reconfiguring to assume optimized form for targeted function. In this talk I shall explain how we mathematically interpret such lessons from nature, and adaptively train deep generative networks, to stably learn to correct form for optimized function, in a number of dynamical scenarios. We exploit the tight connections between discrete and continuous controllable dynamical systems and reinforcement learning. These characterizations are crucial for deriving feasibility and guaranteed convergence (stability), while accelerating the reinforcement learning process.

###### November 10th, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

For UTMail only:

### Brian La Cour: The Quantum Eraser

Have you ever wanted to erase something in the past? An experiment call the quantum eraser seems to do just that. In this talk, I'll discuss the experiment and how we can actually understand it from a simple, classical perspective. You can join in the fun yourself by building and running the experiment with me online using our Virtual Quantum Optics Laboratory at vqol.org

###### November 3rd, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

For UTMail only:

### Jonathan Johnson: Knot Groups and Bi-orderability

Every knot in the 3-sphere (the 3D plane, plus a point “at infinity”) has an associated group which captures a lot of information about the knot. An interesting property of a knot group is whether or not the group admits a total order invariant under both left and right multiplication. This property is called bi-orderability. In this talk, we will discuss how bi-orders on knot groups are constructed; then, we will survey some interesting results in this area of research.

###### October 27th, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

ZOOM ID: 694 684 6598 Password: mathclub

## October 23rd at 15:00 CDT

## Course Schedule Q&A

The course schedule for Spring 2021 gets released this Wednesday. If you have questions about which courses

to take, who to take them with, and what these courses cover, this is the meeting for you! We’ll go over the

math courses in all three divisions - lower, upper, and graduate - and help you figure out a plan for

registration day, in an open Q&A style-meeting. If you’re an older student and you feel

confident about how to prepare for next semester, we encourage you to come to

this meeting to offer your perspective and answer questions.

### Joe Miller: Bose-Einstein Condensates

I will briefly describe the mathematics (and physics) of Bose-Einstein condensates, and talk about some mathematical questions we can ask about them. Very little quantum mechanics will be assumed.

###### October 20th, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

For UTMail only:

### Teddy Weisman: Solving the Word Problem with Geometry

There are some surprising and deep connections between classical ideas in computer science, non-Euclidean geometry, and abstract algebra. We'll get a taste of some of these connections by exploring string-rewriting systems, and thinking about how to understand their computational properties in terms of group theory, metric spaces, and a 2,000-year old geometry problem!

###### October 13th, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

For UTMail only:

## Math Speed Run!

The free use of

terminology and theorems

in talks can often be an issue

for students who are new to math.

Needing to constantly write down

unfamiliar definitions and ask about how certain steps are made can often detract from what students are able to learn from a lecture. Next Friday, we’ll go over many of the important definitions and concepts

on a surface level so that

underclassmen can have a better

idea of what is going on in

talks.

## October 9th at 15:00 CDT

ZOOM ID: 694 684 6598

Password: mathclub

Set Theory

Logic

Proof Methods

Number Theory

Albegra

Analysis

### Neza Zager Korenjak: Hyperbolic Geometry

Ancient Greeks axiomatized Euclidean geometry, but the parallel postulate puzzled them - and centuries of mathematicians to follow - as it seemed like it should be possible to derive it from other axioms. It turns out that not only is this axiom not really needed, but negating it leads to other interesting geometries. We will look at the hyperbolic plane, where we can draw infinitely many lines going through a single point, all parallel to a given line. Strange things can happen here, for example, right-angled pentagons.

###### October 6th, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

For UTMail only:

### Scott Aaronson: The Busy Beaver Frontier

The Busy Beaver function, with its incomprehensibly rapid growth, has captivated generations of computer scientists, mathematicians, and hobbyists. In this talk I'll offer a personal view of the BB function 58 years after its introduction, emphasizing lesser-known insights, recent progress, and especially favorite open problems. Based on his recent survey article.

Zoom ID: 937 4710 6319 Password: mathclub

###### September 29th, 2020 at 17:00 CDT

For UTMail only:

## Game Night!

This will be a social event, and we're going to play virtual games like skribbl.io, codenames, and jackbox. This is a good chance to get to meet each other and the officers if you haven't already, and I can attest that this type of game can be really fun, even if you don't know everyone that well.

## September 29th at 15:00 CDT

ZOOM ID: 694 684 6598 Password: mathclub

### Dr. Dave Rusin: Putnam Competition 2020-21 "What it is, how it will run, and why the Longhorns will win!"

The Putnam Competition is an annual mathematics contest exam taken annually by over 4000 college students in the U.S. and Canada. It is notoriously difficult, but for the right kind of person it's great fun. The University of Texas has done increasingly well in recent years, placing 9th nationwide last year, and we'd love to do even better this year. But the Covid pandemic is necessitating big changes. We'll discuss what's known about the changes so far, and how UT students can participate. We'll also show what kind of problems appear on this test and the type of solution required.

###### September 22nd, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

For UTMail only:

### Hannah Turner: The Borsuk-Ulam Theorem and Ham Sandwiches

The Borsuk-Ulam theorem is about continuous functions from n-dimensional spheres to R^n. It has some corollaries, for example: there are always two points on Earth with the same temperature and pressure. It also shows that given any 2 (very flat) pancakes in the plane, or any 3 ham sandwiches in R^3 we can halve them all at the same time with one slice of the knife. I'll give the idea of the proof of the theorem and these corollaries.

Things you might want to have:

Some familiarity with continuous functions from R to itself

###### September 15th, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub

For UTMail only:

### Tom Gannon: The Mathematics of Voting

We'll talk about the mathematics behind different ways we can vote on things. The main result we'll be discussing is called Arrow's Impossibility Theorem, which roughly speaking, says that there literally cannot exist a perfect voting system.

Things you might want to know:

Induction

Basic Set Theory (Union, Intersection, etc.)

###### September 8th, 2020 at 17:00 CDT

Zoom ID: 937 4710 6319 Password: mathclub