Associate Professor

**Academic family:**

- Bruce C. Berndt — postdoc mentor (University of Illinois at Urbana-Champaign)
- Victor H. Moll — phd advisor (Tulane University)
- Jonathan M. Borwein — phd co-advisor (University of Newcastle)

Previously, I was a J. L. Doob Research Assistant Professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign.

From January to December 2013, as well as in March and April of 2015, I visited the Max Planck Institute for Mathematics.

## Research interests

Analytic number theory, special functions, symbolic and numerical computation, enumerative combinatorics

More specifically, objects of particular interest include

- Apéry-like numbers and their properties, particularly supercongruences,
- modular forms and arithmetic differential equations,
- hypergeometric functions, multiple polylogarithms and Mahler measure.

## Recent publications

- Gessel-Lucas congruences for sporadic sequences

Armin Straub — Monatshefte für Mathematik — 2023 - On the representability of sequences as constant terms

Alin Bostan, Armin Straub, Sergey Yurkevich — Journal of Number Theory — Volume 253, 2023, Pages 235-256 - On congruence schemes for constant terms and their applications

Armin Straub — Research in Number Theory — Volume 8, Number 3, 2022, Pages 1-21, #42 - Sums of powers of binomials, their Apéry limits, and Franel's suspicions

Armin Straub, Wadim Zudilin — International Mathematics Research Notices — Volume 2023, Number 11, 2023, Pages 9861-9879 - Generalized Lucas congruences and linear p-schemes

Joel A. Henningsen, Armin Straub — Advances in Applied Mathematics — Volume 141, 2022, Pages 1-20, #102409

## Recent talks

- Automatic Lucas-type congruences (ACA 2023)

2023/07/19 — ACA 2023 (Applications of Computer Algebra), Session on D-Finite Functions and Beyond: Algorithms, Combinatorics, and Arithmetic (Warsaw, Poland) - Sums of powers of binomials, their Apéry limits, and Franel's suspicions (Dalhousie)

2022/10/06 — Mathematics Colloquium (Dalhousie University) - Gaussian binomial coefficients with negative arguments (South Alabama)

2022/09/29 — Mathematics Colloquium (University of South Alabama) - Sums of powers of binomials, their Apéry limits, and Franel's suspicions (El Paso)

2022/09/18 — AMS Fall Central Sectional Meeting, Special Session on The Intersection of Number Theory and Combinatorics (University of Texas at El Paso) - Sums of powers of binomials, their Apéry limits, and Franel's suspicions (Paris)

2022/07/01 — Joint Seminar: MATHEXP-PolSys & Transcendence and Combinatorics (Inria Saclay & Sorbonne University, Paris)