Sophex is a seminar in the UT math department specifically for first and second years to give talks, attend talks by their peers, and interact in a friendly environment.

A list of previous of activities, speakers and talks is listed below.

## Fall 2023

**2023 - 09 - 01 | Justin Toyota | First-Order Logic and The Compactness Theorem**

The compactness theorem is one of the most classic theorems of first-order logic. Put informally, it tells us that an object exists satisfying an infinite set of axioms if we can find objects satisfying any finite subset of them. In this talk, I will outline a near-topological proof of the compactness theorem and use it to prove that every field has an algebraic closure.

**2023 - 09 - 08 | Ryan Wandsnider | The Pseudo Arc **

The Pseudo-Arc is one of the crown jewels of continuum theory. During the talk, we will give a brief overview of how the Pseudo-Arc is constructed and discuss some of its properties.

**2023 - 09 - 15 | Laney Bowden | Linear Systems of Curves on Abelian Surfaces, but why?**

What is an abelian surface? What is a linear system of curves?? Why would one care about such things??? Well, you’re in luck! We’ll be taking a brief non-technical exploration of the physics and mathematics that motivates studying linear systems of curves on abelian surfaces (i.e string theory, mirror symmetry, geometric Langlands, etc). Time permitting, I will attempt not to bore you with a technical introduction to abelian surfaces.

**2023 - 09 - 22 | Isaac Hellerman | Set: The Game**

We will teach the rules of the card game SET and play a series of rounds to demonstrate. There will also be a brief discussion of the unique algebraic properties of the game in terms of a group action on the SET deck, including an exploration of other sets that have similar properties.

**2023 - 09 - 29 | Sophex cancelled due to The First Great Applied Math Exam**

**2023 - 10 - 06 | Lachlan Potter | Subgroups and Representations of SL_2(Z)**

We introduce the congruence subgroup property (CSP) and polynomial representation growth (PRG) for the class of examples SL_d(Z), including a crash course on representation theory of groups. We discuss the relationship between the CSP and PRG. Finally, we give some brief proof sketches using the examples of SL_d(Z).

**2023 - 10 - 13 | Jay Lee | Improving the Lower Back, Knees, and Ankles With the Squat**

We will be exploring the technique and variations of the squat in this talk. There will be exercises and stretches that will be introduced that I believe can help people address issues in the aforementioned body parts. No physical movement will be required by the audience, but they are welcome to join.

**2023 - 10 - 20 | Christian Liu | Topics in Functional Analysis**

I will be talking about some topics from Applied 1. Like the Barbie movie, this talk is for everyone. If you are in Applied, come to review what we've learned and throw tomatoes at me when I mess things up. If you are not in Applied, come get a preview of what you will learn.

**2023 - 10 - 27 | Zachary Lee | Continuation of fourth order Schrödinger Equation**

The study of unique continuation for partial differential equations (PDE) has historically been an active area of research. These uniqueness results typically assume that two solutions are "close" at two different times and use that to conclude that they are identical on all of their domain.

In this talk, we discuss uniqueness properties of solutions to the fourth-order Schrödinger equations in dimension 2.

We prove that if the difference of two solutions to the linear equation has fast enough decay in a certain Sobolev space, then the two solutions must coincide identically on all of . We then build on this result to show that if the difference of two solutions to the nonlinear equation has fast enough decay in the same space, the two solutions also coincide on all of their domain. We rely on a persistence of decay property and the method of Carleman estimates.

**2023 - 11 - 03 | Audrick Pyronneau | On the Topology of Exotic 4-manifolds**

In this talk we introduce the history of exotic structures and the motivation behind studying 4-manifolds. One of the field's central problems is the famous Poincaré conjecture, to this day the only solved Millennium Prize problem. Throughout the years, solutions to this question in specific dimensions have lead to multiple Fields Medals. In 1982, Freedman proved the conjecture in 4 dimensions, but the 4-D smooth Poincaré conjecture, is still open; in fact, 4 remains the only dimension for which it is unknown whether manifolds homeomorphic to the sphere is also diffeomorphic to it. One way to understand exotic structure is by studying surfaces embedded in 4-manifolds.

**2023 - 11 - 10 | Mark Abate | Git Hub**

Git is a version control tool used by software engineers. In this Sophex talk, I will explain what git and GitHub are and ways you might use them. Feel free to bring a laptop and follow along!

**2023 - 11 - 17 | Mina Parast | Bayesian optimization and Machine Learning**

This talk will be about machine learning problems and Bayesian optimization (BO) which is a useful approach in these problems. Moreover, I want to tell you how we can extend BO to Riemannian manifolds which can be more beneficial than Euclidean BO.

**2023 - 11 - 24 | Happy Thanksgiving! **

**2023 - Dec - 02 | Audrick Pyronneau | End of Semester**

## Fall 2022

** 2022 - 09 - 02 | Zach Richey | Compartmental Models of Disease**

*In this seminar, we will discuss the modelling of disease spread using compartmental models. We'll cover topics including motivating assumptions, deriving the ODEs, nondimensionalization, the basic reproduction number, and equilibrium and stability analysis.*

**2022 - 09 - 09 | Elise Brod | Let's Talk About Set!**

*In particular, let's discuss some mathematical and non-mathematical properties of the game, SET. Some likely topics include: the rules of the game; some basic combinatorial properties of a deck of SET cards; how cap sets relate to geometry, Ramsey theory, and the frustration of SET players everywhere; and some hot-off-the-presses polling data on the prevalence of SET in mathematical households.*

**2022 - 09 - 16 | JiWoong Park | Young Tableaux in Representation Theory**

*Young tableaux is a combinatorial object which has remarkable applications in representation theory and algebraic geometry. What makes it even more remarkable is that at first sight Young Tableaux does not seem as a serious mathematical object at all. In this talk I’ll give a brief overview of how Young tableaux is related to representation theory of Lie algebras (and quantum groups if time permits). It is a primary example of combinatorial representation theory. Young_Tableaux_in_Representation_Theory.pdf*

**2022 - 09 - 23 | Toby Aldape | Lean**

*Lean is a proof assistant created to help mathematicians formalize proofs of mathematical results. We will be talking about why mathematicians care about proof assistants, some of the history of the subject, and learning the basics of Lean by playing the Natural Number game located on the website of mathematician Kevin Buzzard. Bring a laptop and be prepared to have fun!*

**2022 - 09 - 30 | William "Winston" Winston | The Topology and Algebra of the Braid Group**

*In spite of its simple and intuitive definition, the braid group mysteriously shows up in unexpected areas in mathematics. We first unravel some incarnations of the braid group in studying the "symmetry group" of surfaces. We then see how "braiding group elements" is of intrinsic interest in group theory. We close with an application in graph theory.*

**2022 - 10 - 08 | Jeffrey Cheng | Convolution**

*The talk will be an introduction to convolution. In particular, I will introduce what the convolution of two functions is, and talk about its applications to some density results. Then, I will introduce discrete convolution, and talk about its application to image processing. Finally, we'll have some fun convolving images.*

**2022 - 10 - 14 | Luisa Velasco | Calculus of Variations**

*This talk will be an introduction to the basic problem and the classical methods of calculus of variations. Specifically, we will derive the Euler-Lagrange equation and discuss several well-known example problems. Lastly, we'll look at how these methods are used in physics, particularly in theoretical mechanics and general relativity.*

**2022 - 10 - 21 | Will Ghanem | The Word Problem and Hans Niemann**

*In this talk we discuss the word problem and Hans Niemann.*

**2022 - 10 - 28 | Alborz | Platonism**

*Is Math created by us or discovered? In this talk I’d like to present some of my recent readings and understanding of the platonism in math and its take on philosophy of math as well as several objections raised to this view.*

**2022 - 11 - 05 | Isaac | Singularities in Prime Characteristic**

**2022 - 11 - 12 | Remy | TBD**

*TBD*

**2022 - 11 - 19 | Jiayun | TBD**

*TBD*

**2022 - 11 - 26 | Turkey Day | Anatolia and Eastern Thrace**

*Go away and think upon all that gives ye thanks*

**2022 - 10 - 12 | Abhishek Koparde | TBD**

*TBD*

## Fall 2018

Date |
Speaker |
Title |

09/07/2018 | Tynan Ochse | p-adic Differentiation |

09/14/2018 | Charlie Reid | The Tropical Grassmannian is Tree Space |

09/21/2018 | Will Stewart | Lie algebras and their role in conformal field theory |

09/28/2018 | Joe Jackson | Excited Random Walks and their Asymptotics |

10/05/2018 | Shiyu Liang |
Non-left orderable surguries on 1-bridge braids |

10/12/2018 | Joe Miller | On Kakeya sets |

10/19/2018 | Sean Sommers | Forecasting Methods in Time Series Analysis |

10/26/2018 | Natalie Hollenbaugh | The Ideal Class Group and Fermat's Last Theorem |

11/02/2018 | Daniel Restropo Montoya | Critical points and symmetries in PDE |

11/09/2018 | Alberto San Miguel | Cayley Graphs |

11/16/2018 | Kai Nakamura | Mapping Class Groups of Surfaces |

11/23/2018 | No Sophex due to Thanksgiving break | |

11/30/2018 | Casandra Monroe | Turing Machines™ and their properties |

12/07/2018 | No Speaker (Crown) | No speaker for the last week of classes, we'll have Sophex at the crown this week |

## Spring 2018

Date |
Speaker |
Title |

01/26/2018 | Austin Alderete | A matrix classification of Capell-Shaneson spheres |

02/07/2018 | Rok Gregoric | Operads are Rad! |

02/09/2018 | Rok Gregoric | A gentle introduction to spectra |

02/16/2018 | Richard Wedeen | Clifford Algebras |

02/23/2018 | Dan Weser | The Extension Problem for Elliptic PDEs |

## Fall 2017

Date |
Speaker |
Title |

9/8/2017 | Riley Zeigler | Norm-Perfect Numbers |

9/15/2017 | Rok Gregoric | Loops, representations, and Riemann-Roch |

9/22/2017 | Jincheng Yang | Stability and instability of shear flow in a rotating system |

9/29/2017 | Dan Weser | Crash Course in Optimal Transport |

10/6/2017 | Riccardo Pedrotti | A Very Brief Introduction to Stable Classification of 4-Manifolds |

10/13/2017 | Richard Wedeen | Fundamental Groups, Galois Groups, and Riemann Surfaces |

10/20/2017 | Nes Sansawang | |

10/27/2017 | Ruhui Jin | |

11/3/2017 | Danielle King | |

11/10/3017 | Alain Olavarrieta | |

11/17/2017 | Amit Adhikari | |

11/24/2017 | No Speaker | (Thanksgiving) |

12/1/2017 | George Torres | |

12/8/2017 |

## Spring 2017

Date | Speaker | Title |
---|---|---|

1/27/2016 | Sebastian Schultz | Quiver Representations |

2/3/2017 | Darren King | Viscosity Solutions in PDE |

2/10/2017 | Tom Gannon | The Artin-Schreier Theorem |

2/17/2017 | Kenny Schefers | The Milnor Fibration and Singularities of Complex Hypersurfaces |

2/24/2017 | Keyi Wu | Introduction of Sampling Methods for Uncertainty Quantification |

3/3/2017 | Yixian Wu | Introduction to p-Adic Numbers |

3/10/2017 | Ruth Navarre | Moment Generating Functions |

3/17/2017 | (No Speaker) | Spring Break |

3/24/2017 | Teddy Weisman | |

3/31/3017 | Tom Gannon | |

4/7/2017 | Maria Soria Carro | |

4/14/2017 | Neža Zager Korenjak | |

4/21/2017 | Shalin Parekh | |

4/28/2017 | Ignacio Tomasetti | |

5/5/2017 | Michael Hott |

## Fall 2016

Date | Speaker | Title |
---|---|---|

9/2/2016 | Tom Gannon | Measurability and the Banach-Tarski Paradox |

9/9/2016 | Austin Alderete | A Vanishing Bridge: Hilbert's Link Between Algebra and Geometry |

9/16/2016 | Neža Žager Korenjak | Theorems on Compactness |

9/23/2016 | Jay Hathaway | Representation Theory and Spectroscopy |

9/30/2016 | Teddy Weisman | Spectral Graph Theory and Expander Derandomization |

10/7/2016 | Michael Hott | Rearrangement Inequalities |

10/14/2016 | Johnathan Johnson | The Alexander Polynomial of a Knot via Siefert Surfaces |

10/21/2016 | Kendric Schefers | Proving Kneser's conjecture using the Borsuk-Ulam Theorem |

10/28/2016 | Gillian Grindstaff | Phylogenetic Trees and Operads |

11/4/2016 | Ivan Tulli | Intro to Hamiltonian Mechanics and Quantum Mechanics |

11/11/2016 | Yixian Wu | Elliptic Curves and Its Application in Integer Factorization |

11/18/2016 | Shalin Pareleh | Scaling Limits of Random Curves and Interfaces |

11/25/2016 | None | THANKSGIVING |

## Spring 2016

Date | Speaker | Title |
---|---|---|

1/29/2016 | Jonathan Johnson | Summation Chains of Sequences |

2/5/2016 | Max Riestenberg | Intro to Mapping Class Groups |

2/12/2016 | Gillian Grindstaff | Semi-Dispersing Billiards |

2/19/2016 | Andy Ma | Applications of Analysis |

2/26/2016 | Richard Wong | Topological Data Analysis |

3/4/2016 | Yanlin Cheng | A Brief Talk About Schrodinger's Equation |

3/11/2016 | Hannah Turner | Constructions/Decompositions of Some 3-Manifolds |

3/18/2016 | None | SPRING BREAK!! |

3/25/2016 | Frank Lin | Ergodic Theory on the Circle |

4/1/2016 | Tom Oldfield | Applying the Euler-Oldfield Theorem to Property P Groups |

4/8/2016 | Arun Debray | The Mathematics of Functional Programming |

4/15/2016 | Ivan Tulli | Intro to Lagrangian Mechanics and Noether's Theorem |

4/22/2016 | Martin Bobb | Teichmuller Space |

4/29/2016 | Matt Rosenzweig | Bochner-Riesz Multiplier Conjecture |

## Fall 2015

Date | Speaker | Title |
---|---|---|

9/4/2015 | Max Riestenberg | Mathematics in Music Theory |

9/11/2015 | Nick Crispi | Topological Transitivity in Discrete Dynamical Systems |

9/18/2015 | Richard Wong | Algebraic Struction of the Rubik's Cube |

9/25/2015 | Jonathan Johnson | Introduction to Game Theory |

10/2/2015 | Tom Oldfield | Sheaves - How to Glue in Geometry |

10/9/2015 | Michael Starkey | Quantum Computing and the Deutsch Josza Quantum Algorithm |

10/16/2015 | Jonathan Johnson | More Game Theory |

10/23/2015 | Isaac Smith | Ultrafilters |

10/30/2015 | Hannah Turner | An Erdos Conjecture |

11/06/2015 | Gill Grindstaff | Trees and Tree Covers |

11/13/2015 | Arun Debray | The Grothendieck Group |

11/20/2015 | Katie Mount | Life Contingency |

12/4/2015 | Adrian Clough | Yoneda's Lemma |

## Spring 2013

Date | Speaker | Title |
---|---|---|

1/18/2013 | Organizational Meeting | |

1/25/2013 | Javier Morales | Calibrated complex structures on the space of Hermitian matrixes with a fixed spectrum of distinct eigenvalues |

2/1/2013 | Luis Duque | Some stuff about non-necessarily associative (NNA) algebras |

2/8/2013 | Cornelia Mihaila | Hypergraphs and their applications |

2/15/2013 | Allison Miller | Tangles, ravels, and spatial graphs |

2/22/2013 | Soledad Villar | The congruent number problem |

3/1/2013 | Valentin Zakharevich | Introduction to Model Theory |

3/8/2013 | Tianran Geng | Why is pi irrational? |

3/15/2013 | Spring break: no Sophex seminar | |

3/22/2013 | Richard Hughes | Deformation Cohomology |

3/29/2013 | Tim Carson | Modal Logic |

4/5/2013 | Tim Magee | Cluster algebras and the Laurent phenomenon |

4/12/2013 | Pulak Goswami | Optimizing Insider Information |

4/19/2013 | Robin Neumayer | An Introduction to Optimal Transport |

4/26/2013 | Roman Fayvisovich | The Fundamental Theorem of Asset Pricing |

## Fall 2012

Date | Speaker | Title |
---|---|---|

9/7/2012 | Valentin Zakharevich | Basic Geometric Probability |

9/21/2012 | Robin Neumayer | Traversing the Pachner Graph |

9/28/2012 | Allison Miller | Asymptotic Density of Wecken Maps |

10/5/2012 | Tim Carson | The Homotopy Method for Eigenvales of Symmetric Matrices |

10/12/2012 | Yaroslav Vergun | Completeness in Riemannian Manifolds |

10/19/2012 | Michael Wong | The Riemann-Roch Theorem for Compact Riemann Surfaces |

10/26/2012 | Sara Cohen | Bistellar Equivalences of Two Families of Simplicial Complexes |

11/2/2012 | Soledad Villar | Dimension of Modular Form Spaces |

11/9/2012 | Tim Magee | Topological Quantum Field Theories |

11/16/2012 | Keren Li | The Jones Polynomial: A Magnificent Invariant on Knots and Links |

11/30/2012 | Rustam Antia-Riedel | An Introduction to Chern-Weil Theory (Maybe) |

## Spring 2012

Date | Speaker | Title |
---|---|---|

1/27/2012 | Rahul Shah | Intro to Quantum Mechanics for Mathematicians |

2/3/2012 | Adam Hughes | An Introduction to Number Theory |

2/10/2012 | Lee Cohn | Covering Spaces from a Categorical Viewpoint |

2/17/2012 | Roberta Guadagni | The Seifert Surface of a Knot |

2/24/2012 | Michelle Chu | The Complement of the Figure-8 Knot |

3/9/2012 | Dennis Kriventsov | Calculus on Fractals |

3/23/2012 | Julia Bennett | Symplectic Vector Spaces |

3/30/2012 | Claudia Raithel | Lagrange's Four Squares Theorem via Minkowski's Theorem |

4/6/2012 | Yimin Zhong | Log-concavity and Fundamental Gap conjecture |

4/20/2012 | Sona Akopian | TBA |

4/27/2012 | Aaron Fenyes | TBA |