Howard University - Mathematics Colloquium - Fall 2026

• 21 August 2026
  
  Speaker: Dennis Davenport, Howard University.
  Title: Riordan Arrays, Pseudo-Involutions, and AI-Assisted Mathematical Discovery
  Click to read the Abstract.
  The Riordan group is a group of infinite lower triangular matrices that are defined by two generating functions, g and f. The kth column of each matrix has a generating function related to $gf^k$. There are many applications of Riordan arrays, among other things they can be used to count combinatorial objects and to prove combinatorial identities. In this talk, I will introduce Riordan arrays and discuss recent joint work with Dewayne Dixon and Moussa Doumbia on pseudo-involutions. In the Appell subgroup, the pseudo-involution condition reduces to the simple identity $g(z)g(-z)=1$, which leads to a useful classification and several interesting integer sequences. I will also discuss how artificial intelligence can assist mathematical discovery by helping generate examples, identify patterns, and suggest conjectures, while exact computation and proof remain essential.
• 28 August 2026
  
  Speaker: Roberto De Leo, Howard University.
  Title: Free maps on tori in critical dimension
  Click to read the Abstract.
  In Differential Geometry several important objects are defined via some Partial Differential Inequality. For instance, given a manifold $M$ and a map $f:M \to R^q$, we say that $f$ is an immersion if the matrix of its first partial derivatives has maximal rank at every point. Similarly, we say that $f$ is free if the matrix of its first and second partial derivatives has maximal rank at every point. While it is easy to show that there can be no immersion of the 2-torus $T^2$ in $R^2$, which is the "critical dimension" case for immersions, it is not that simple to find out about the existence of free maps $f:T^2\to R^5$, which is the "critical dimension" case for free maps. The question of the existence of free maps $f:T^2\to R^5$ was posed in Eighties independently by M. Gromov and Y. Eliashberg. I recently showed that there exist such maps by devising an algorithm able to generate some class of such maps. In this talk I will first illustrate in an elementary way the role of free maps in Riemannian geometry and, more generally, in Gromov's "holonomic principle" theory and then show a simple method to generate free maps $T^2 \to R^5$. I will also illustrate the role played by AI in this breakthrough.
• 4 September 2026
  
  Speaker: Cheikh Ndiaye, Howard University.
  Title: Mass, Interaction, and Uniformization in Conformal Geometry
  Click to read the Abstract.
  In this talk, we explore natural extensions of the classical Uniformization Theorem through the lens of the Yamabe problem and its modern generalizations. Our goal is to highlight how ideas of mass and interaction arise in conformal geometry and how they shape the analysis of curvature equations. I will survey key techniques, describe several geometric phenomena that emerge in higher dimensions, and outline recent advances in the study of these problems. The talk is intended to be broadly accessible to a general mathematics audience.
• 11 September 2026
  
  Moderator: Angelica Babei, Howard University.
  Title: Forum on AI, math, and ethics
  Click to read the Abstract.
  On Tuesday, OpenAI announced that an internal AI model obtained a solution to the Navier-Stokes problem, one of the Millennium Prize Problems. However, the announcement was marked by controversy because, shortly before, Tristan Buckmaster, a math professor at NYU, announced his related work with Levent Alpoge, a researcher at Anthropic, and accused OpenAI of serious ethical and academic misconduct. In lieu of a traditional colloquium talk this week, Angelic Babei, an assistant professor in the Howard math department whose research touches on AI in math, will moderate an open forum about these developments and more generally the importance of ethics and academic norms when using AI for math. We invite all those who attend to join in on the discussion.
• 18 September 2026
  
  Moderator: Dennis Davenport, Howard University.
  Title: Forum on AI and math, continued
  Click to read the Abstract.
  Dr.'s Bourama Toni and Dennis Davenport from the Howard math department will continue the forum on AI and math from last week. The conversation will be expanded to include topics like teaching undergraduate math, and training math graduate students, in the age of AI. As before, all are welcome to join the discussion.
• 25 September 2026
  
  Speaker: Olga Bernardi, University of Padova (Italy).
  Title: A Walk Through Mathematical Billiards
  Click to read the Abstract.
  The seminar aims to introduce the most widely studied models of mathematical billiards. We then explain and discuss basic concepts such as integrability, existence of periodic orbits, spectrum, and the inverse problem of reconstructing the billiard table. Finally, we recall some of the most famous conjectures concerning these intriguing dynamical systems.
• 2 October 2026
  
  Speaker: Charles Burnette, (Xavier U. of Louisiana).
  Title: TBA
  Click to read the Abstract.
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• 9 October 2026
  
  Speaker: Manami Roy, Lafayette College.
  Title:
  Click to read the Abstract.
  This chat-like presentation, accessible to undergraduate students, discusses the Poincarè Harmonic Oscillator and its variants, fundamental models in dynamical systems for symmetry, stability, periodicity and quasi/almost-periodicity. From its general description by the second order ODE $\ddot x+\omega^2(t)x^2(t)=f(t)$ we explore respectively its Archimedean phase-space formulation in real continuous time, its Non-Archimedean (p-adic) and quantum formulation. The geometry of motion and phase-space topology transform from the real (continuous circular flows in $\mathbb R^2$) to the p-adic domain (ultrametric tiles in $Q^2_p$). Smooth sinusoidal solutions and elliptical orbits over the reals versus solutions in power series of p-adic trigonometric functions $\sin_p(\omega t)$ and $\cos_p(\omega t)$ on finite convergence disks representing locally constant, hierarchical and discretized motion in p-adic time.
• 17 October 2026
  
  Speaker: , .
  Title:
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• 23 October 2026
  
  Speaker: , .
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• 30 October 2026
  
  Speaker: , .
  Title:
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• 6 November 2026
  
  Speaker: , .
  Title: TBA
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• 13 November 2026
  
  Speaker: , .
  Title: TBA
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  TBA
• 20 November 2026
  
  Speaker: , .
  Title: TBA
  Click to read the Abstract.
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