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Wenhua Zhao Algebraic-Geometry Seminar

Wenhua Zhao“My research interests are mainly on polynomial automorphisms and the Jacobian conjecture. My earlier research also involves Vertex Operator Algebra and Conformal Field Theory”.
Wenhua worked on a new notion of Mathieu subspaces, which he introduced in 2009.
April 2, 1968 – Dec. 23, 2023For updates: signup to the WZ-AGS-Newsletter (email organizers).

This is a traditional seminar with a Theme: Belyi Theorem, as a central result bridging Algebraic Number Theory (Number Fields) and Algebraic Geometry (Riemann Surfaces and Function Fields). It is a Mathematical Model for baryons, as an application to Elementary Particle Physics.

… and a Team: Lucian M. Ionescu, ISU (organiser); Charlotte Ure, ISU; Prof. Gabriel Pripoae, Bucharest University, Romania (Diff. Geometry and General Relativity specialist); Prof. Dr. Bertrand Eynard, I. Ph. T. CES, Saclay, France (Math-Physicist, author: Lecture Notes on Riemann Surfaces, Counting Surfaces).

Spring 2024

Meeting times: Th. 10:00 a.m.-12:00 pm, STV 120 – please ask for a Zoom link if interested (recordings are stored for 30 days in the Cloud: see the corresponding link after the run of the seminar).

  • 2/15 Organizational Meeting, plan and resources: ISU Milnor Library Counting Surfaces; keywords: covering maps, branched covers, function fields (for algebraic RS), number fields etc.
    • Goals: study AG-Tools and Methods (R&D in Math) with applications in Chemistry/Physics;
    • Format: 1st hour presentations; 2nd hour discussions (“Lecture-Recitation”);
    • Plan: presentations from “Counting Surfaces” (B.E.), relating topics (LI), formal aspects (CU) etc;
  • 2/22 L. M. Ionescu, “Belyi Maps: a brief Math-Physics motivation and overview” (see also [1] for additional details); we will watch John Voight’s YT survey (10-20 min; pdf here) followed by some explanations and background. Discussions are encouraged.
  • 2/29 B. Eynard, “Maps and Discrete Surfaces; Riemann surfaces” (I) from Counting Surfaces, Ch. 1,2 & 6 (see [2]).
  • 3/7 C. Ure, “Function fields in number theory and geometry”, Abstract: Function fields have many applications in various areas of mathematics. Often, they can be employed to translate a geometric problem to a purely algebraic one. In this talk, we will discuss the basic notions of function fields in the context of Riemann surfaces and arithmetic curves. If time permits, connections to zeta functions will be discussed. This talk is accessible to undergraduate and graduate students. Rec/Pwd.
  • 3/21 L. M. Ionescu “Covering maps, branched covers and Riemann-Hurwitz Formula; on function/number fields connection”, Ramified coverings of Riemann surfaces over number fields encode topologically and algebraically a Gauge Theory with singularities (sources). We will recall covering spaces, ramification and interpret as dynamics: “cars flowing on a network” (Poincare-Hopf Theorem) and intuitively as “traveling in a multi-level building” to help our intuition about a very rich Math framework.
  • 3/28 L.M. Ionescu, The connection between Matrix Integrals and Belyi’s Theorem will be reviewed, motivating the importance of understanding the connection between function fields and number fields, via Hodge-de Rham Theory and periods.
  • 4/4 SPECIAL EVENT – Conference Catherine Goldstein and Clemence Perronnet at IHES, 10:30 am ->?, via Zoom. Viewers of the event in STV 120, are invited to an open discussion afterwords :
    • Title: “The role that female role models can play in advancing equality in science”
    • Abstract: “After its visit to the Lumen of the University of Paris-Saclay, the exhibition Just Do Maths! will travel to IHES and will be inaugurated by a conference by Catherine Goldstein and Clémence Perronnet on the role that female role models can play in advancing equality in science. This conference is based on the book “Matheuses” which has just been published by the CNRS. “
    • Language: French (probably);
    • Event online via Zoom.
    • Post-event YT recording.
  • 4/11 Break – no seminar; preparing a “new series” …

New Series

Rethinking the targeted audience and format: we will try presentations of a subject / topic (AG/Belyi Map theme), including a student oriented learning component, presentation of an article with several segments (presentations) … (details will follow).

  • 4/18 (Special event) L. M. Ionescu, Rethinking the Real Numbers, presented in the Pure & Applied Math Seminar @12:00, STV 136B.
  • 4/25 No seminar
  • 5/2 (Special event) Anurag Kurumbail, Title: “A Modular Group construction of Real Numbers“, MAT 490 Master Project Presentation;
    • Abstract: The Continued Fractions representations of Real Numbers provides a deeper understanding of many classes of numbers, including quadratic irrational numbers. A norm-free construction of real numbers is presented, using the modular group PSL(2;Z). It defines a Sequential Space extending the rational numbers. The theory of extensions of Sequential Spaces is developed to include the former construction. An application of the modular group representation of real numbers to quadratic irrational numbers, yields new results in the theory of Number Fields.
    • Presentation will be @12:00 in STV 136B.

[1] L. M. Ionescu, The Beauty and The Beast (preliminary motivation); additional details: Algebraic-Geometric Tools for Particle Physics, https://vixra.org/abs/2305.0001
[2] B. Eynard, Counting Surfaces,  Progress in Mathematical Physics (PMP, volume 70).
[3] John Voight, “Belyi Maps in Number Theory: a survey“, YT presentation, 2021; pdf.
[4] …

For updates and comments, email LMI.

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