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Counting problems

Many problems in number theory can be phrased as counting problems. How many solutions are there to this Diophantine equation? How many values of this polynomial are perfect squares? How many of these exponential sums are large? We will give a taste of several, quite different, counting problems with connections and applications ranging from algebraic [Read More...]

Presenter: Lillian B. Pierce, Duke University
Symposium Year: 2023
Session: Plenary Lecture
Presentation Time: September 30, 2023; 8:45 am

Exploring Bridge Program Participants' Sense of Belonging and Identity in Mathematics

There are many ways that institutions of higher learning aim to address attrition rates and lack of diversity in STEM. Studies show that sense of belonging in mathematics may impact students’ desire to persist in STEM. Summer bridge programs are one resource used to improve retention in STEM by helping students become acclimated to STEM in college. This [Read More...]

Presenter: Skylyn Irby, The University of Alabama
Authors: Skylyn Irby
Symposium Year: 2023
Session: Pure and Applied Talks by Mathematicians Enhancing Diversity in Graduate Education (EDGE) [Organized by Quiyana M. Murphy and Sofía Martínez Alberga]
Presentation Time: September 30, 2023; 9:45 am

Energy and Discrepancy on Hamming Spaces

In 1973, Stolarsky discovered a connection between the quadratic spherical cap discrepancy of a point set on the sphere, and it's sum of Euclidean distances between pairs of distinct points, showing that minimizing the discrepancy was equivalent to maximizing the sum of distances. In this talk, we discuss an analogue of this result for the Hamming [Read More...]

Presenter: Ryan W Matzke, Vanderbilt University
Symposium Year: 2023
Session: Special Session on Discrete Harmonic Analysis [Organized by Christina Giannitsi and Michael Lacey]
Presentation Time: September 30, 2023; 9:45 am

Local heights computations for quadratic Chabauty

The method of quadratic Chabauty was a groundbreaking development on the problem of explicitly determining the set of rational points on a curve. A crucial step of this method is the computation of values of local height functions at primes of bad reduction. In this talk, I will discuss algorithms and provide practical examples of computing these local [Read More...]

Presenter: Juanita Duque-Rosero, Boston University
Authors: Alexander Betts, Juanita Duque-Rosero, Sachi Hashimoto, and Pim Spelier.
Symposium Year: 2023
Session: Recent Advances in Curves and Abelian Varieties [Organized by Renee Bell, Padmavathi Srinivasan, and Isabel Vogt]
Presentation Time: September 30, 2023; 9:45 am

Existence Theory of Multi-Scale Interface Coupling between Deformable Porous Media and Lumped Hydraulic Circuits

We consider an elliptic-parabolic coupled partial differential equation connected to a nonlinear ODE through an interface. The model describes fluid flowing through biological tissues with the ODE accounting for global features of blood flow that affect the tissue. We discuss a modeling choice on the interface coming from the fact that the ODE is 0D and the [Read More...]

Presenter: Sarah Strikwerda, University of Pennsylvania
Authors: Lorena Bociu, Matthew Broussard, Giovanna Guidoboni
Symposium Year: 2023
Session: Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]
Presentation Time: September 30, 2023; 9:45 am

A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem

Group-based cryptography is a relatively unexplored family in post-quantum cryptography, and the so-called Semidirect Discrete Logarithm Problem (SDLP) is one of its most central problems. However, the complexity of SDLP and its relationship to more well-known hardness problems, particularly with respect to its security against quantum adversaries, has not [Read More...]

Presenter: Delaram Kahrobaei, The City University of New York (QC, GC), University of York (UK)
Authors: Christopher Battarbee, Delaram Kahrobaei, Ludovic Perret, Siamak F. Shahandashti
Symposium Year: 2023
Session: Women in Quantum Algorithms and Computing (WQAC) [Organized by Sarah Chehade]
Presentation Time: September 30, 2023; 9:45 am

Mapping Class Groups of Infinite Graphs

Recently, Algom-Kfir and Bestvina introduced mapping class groups of locally finite graphs as a proposed analog of the outer automorphism group of a free group in the infinite-type setting. In this talk, we will introduce infinite-type graphs, their mapping class groups, and why we consider these to be the "big" analog of Out(F_n). Using a [Read More...]

Presenter: Hannah Hoganson, University of Maryland
Authors: George Domat, Sanghoon Kwak
Symposium Year: 2023
Session: Women in Groups, Geometry, and Dynamics [Organized by Hannah Hoganson and Rylee Lyman]
Presentation Time: September 30, 2023; 9:45 am

Hierarchical nonnegative tensor factorizations and applications

Nonnegative matrix factorization (NMF) has found many applications including topic modeling and document analysis. Hierarchical NMF (HNMF) variants are able to learn topics at various levels of granularity and illustrate their hierarchical relationship. Recently, nonnegative tensor factorization (NTF) methods have been applied in a similar fashion in order [Read More...]

Presenter: Jamie Haddock, Harvey Mudd College
Authors: Deanna Needell, Joshua Vendrow
Symposium Year: 2023
Session: Tensor Methods for data modeling [Organized by Anna Konstorum]
Presentation Time: September 30, 2023; 9:45 am

Roundtable: Constructing an “Elevator Pitch”

In academia and industry, one needs to be able to concisely explain their work and its relevance. We often practice formal communication techniques in preparation for research talks, posters, and publications. However, honing informal or impromptu discussions is often neglected. Interviewing and networking highlight the importance of being able to translate [Read More...]

Presenter: Matt Sammons, Metron, Inc.
Authors: Matt Sammons, Brooke Ogrodnik
Symposium Year: 2023
Session: Panels, Roundtables, and Other Events
Presentation Time: September 30, 2023; 9:45 am

Management of Biological Systems Utilizing Mathematical Analysis and Numerical Simulations

Often when building a model and exploring a biological question, we consider how to implement management options and what is the best way to optimize. There are many different methods for incorporating management into a model, we will focus on aspects of control theory. For the talk, we take a model of an invasive pest using nonlinear positive difference [Read More...]

Presenter: Christina J. Edholm, Scripps College
Authors: Chris Guiver, Richard Rebarer, Brigitte Tenhumberg, Stuart Townley,
Symposium Year: 2023
Session: Women in Mathematical Biology: Computation and Modeling [Organized by Katharine Gurski and Yeona Kang]
Presentation Time: September 30, 2023; 9:45 am

An Integrated Approach to the Design of Compact and Connected Reserve Systems

Protected areas for biological conservation depend on large, connected, and compact regions encompassing diverse species. Optimization models have been developed to allocate limited resources efficiently. Initial models focused on protecting most species but resulted in small, scattered areas. Later models aimed to create extensive, compact areas and connect [Read More...]

Presenter: Lakmali Weerasena, University of Tennessee at Chattanooga
Authors: Lakmali Weerasena, Douglas Shier, David Tonkyn, Mark McFeaters, Christopher Collins
Symposium Year: 2023
Session: Exploring the Intersection of Mathematics and Ecology: Research Applications and Findings [Organized by Lakmali Weerasena and Maeve McCarthy]
Presentation Time: September 30, 2023; 9:45 am

Degree $d$ points on plane curves

Given a plane curve $C$ defined over $\mathbb{Q}$, when the genus of the curve is greater than one, Faltings' theorem tells us that the set of rational points on the curve is finite. It is then natural to consider higher degree points, that is, points on this curve defined over fields of degree $d$ over $\mathbb{Q}$. We ask for which natural numbers $d$ [Read More...]

Presenter: Lea Beneish, University of North Texas
Authors: Lea Beneish and Andrew Granville
Symposium Year: 2023
Session: Rethinking Number Theory [Organized by Deewang Bhamidipati, Eva Goedhart, and Amita Malik]
Presentation Time: September 30, 2023; 9:45 am

The rainbow saturation number is linear

Given a graph H, we say that an edge-coloured graph G is H-rainbow saturated if it does not contain a rainbow copy of H, but the addition of any non-edge in any colour creates a rainbow copy of H. The rainbow saturation number rsat(n, H) is the minimum number of edges among all H-rainbow saturated edge-coloured graphs on n vertices. We prove that for any [Read More...]

Presenter: Natasha Morrison, University of Victoria
Authors: Joint work with Natalie Behague (University of Victoria), Tom Johnston, (University of Bristol) Shannon Ogden (University of Victoria), and Shoham Letzter (University College London)
Symposium Year: 2023
Session: Extremal and Probabilistic Combinatorics [Organized by Jinyoung Park and Corrine Yap]
Presentation Time: September 30, 2023; 9:45 am

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