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 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 |