LabAGTA

Events

1. LabAGTA Seminar: Louis H. Kauffman (University of Illinois Chicago), October 29, 2024, 16:00-17:00.
   Title: Generalized colorings, Penrose formulas and multiple virtual knot theory.
   Abstract: This self-contained talk discusses a generalization of virtual knot theory. Multi-virtual knot theory uses a multiplicity of types of virtual crossings. As we will explain, this multiplicity is motivated by the way it arises first in a graph-theoretic setting. As a consequence, we begin with graph theory, and then proceed to the topology. We begin by discussion on the work of Roger Penrose in his paper "Applications of Negative Dimensional Tensors" which contains a remarkable method for counting the Tait colorings of a planar cubic graph. We generalize the Penrose formula to colorings of arbitrary cubic graphs and generalized colorings of cubic graphs with specific perfect matchings. These graph theoretic explorations are of interest in their own right and they involve a use of multiple virtual crossings that sows the seed for the multi-virtual knot theory. [pdf of slides]
   
   
2. LabAGTA Seminar: Louis H. Kauffman (University of Illinois Chicago), October 29, 2024, 13:00-14:00.
   Title: The Mobius function and the Riemann Hypothesis.
   Abstract: This is an elementary talk about the Mobius function and its role in elementary number theory and its relationship with the Riemann Zeta function. We show how, via the structure of Legendre's prime counting function, the Mobius function is expressed recursively in terms of itself. This recursion shows clearly how the Mobius function is far from random. It is more like a magic coin that will not tolerate long runs of heads (+1) or tails (-1). Thus Mobius behaves more sedately than a simple random coin. This gives a heuristic argument in favor of the Riemann Hypothesis. We will discuss these matters with the help of the computer. [pdf of slides]
   
   
3. LabAGTA Seminar: Michael Tsatsomeros (Washington State University, Pullman), November 3, 2023, 13:45-14:45.
   Title: Rank one perturbations for cone reachability and holdability.
   Abstract: A choice of feedback control in a linear control system is proposed in order for the trajectory to eventually enter the nonnegative orthant and remain therein for all time thereafter. This is achieved by imposing the strong Perron-Frobenius property and involves altering the eigenvalues, as well as the left eigenvectors via rank one perturbations.
   
   
4. LabAGTA Seminar: Mihir Kumar Chakraborty (Jadavpur University, Kolkata), May 12, 2023, 15:30-16:30.
   Title: Some aspects of mathematical pluralism.
   Abstract: In this talk, I will provide examples of plurality in mathematics caused because of both the internal as well as external reasons. Thus it will be argued that culture, being understood in a wider sense, plays a significant role in the creation and development of mathematical notions. Recent research called ``Mathematical practices'' and ``Proof events'' may also have justification from this perspective of multiplicity. As a result, from the angles of content and method current uniformity all over the world needs a critical review.
   
   
5. LabAGTA Seminar: Christian Kassel (CNRS and Universite de Strasbourg), March 21, 2023, 15:00-16:30.
   Title: On combinatorial zeta functions.
   Abstract: A generating function is a way of encoding an infinite sequence of numbers by a formal power series. There are various types of such functions. In my talk I will concentrate on one of them called zeta functions and exhibit several examples of interest. In some emblematic cases which I will describe such zeta functions are rational functions. Finally I will present an idea of Kontsevich which leads to a class of zeta functions which are algebraic functions.
   
   
6. Logic and Formal Methods, UNILOG ATHENS 2022, September 22, 2022.
   Morning session (on line, https://centralntua.webex.com/meet/pstef), 09:30-12:30.
   Razvan Diaconescu (invited).
   Maria Dimarokgona, Asterios Gatzounis, Theodoros Mitsikas, Giorgos Pitsiladis, Dimitris Zafirakopoulos, Foivos Skarpelos, Iakovos Ouranos, Dimitra Serakioti, Kostas Barlas.
   Afternoon session (Teleteaching Room, Library N.T.U.A., Multimedia Center), 14:00-18:00.
   Jean Yves Beziau (invited).
   Ioannis Kiouvrekis, Katerina Ksystra - Nikos Triantafyllou, Sofia Almpani, Manthos Bournazos, Ioannis Vandoulakis.
   Round table discussion.
   
   
7. LabAGTA Seminar: Khaled Bataineh (Jordan University of Science and Technology), April 14, 2022, 11:30-12:30.
   Title: New polynomial invariants of knotoids and the theory of polar knots.
   Abstract: We introduce new polynomial invariants for both planar knotoids and spherical knotoids. To introduce these invariants, we first introduce what we call polar knots, and give the fundamentals of their theory.
   
   
8. LabAGTA Seminar: Paolo Cavicchioli (University of Modena), March 31, 2022, 11:30-12:30.
   Title: An algorithmic method to compute plat-like Markov moves for genus two 3-manifolds.
   Abstract: The talk deals with equivalence of links in 3-manifolds of Heegaard genus 2. Starting from a description of such a manifold introduced in [1], that uses 6-tuples of integers and determines a Heegaard decomposition of the manifold, we construct an algorithm (implemented in c++) which allows to find the words in B_{2, 2n}, the braid group on 2n strands of a surface of genus 2, that realizes the plat-equivalence for links in that manifold. In this way, we extend to the case of genus 2 the result obtained in [2] for genus 1 manifolds. We describe in particular a case of this construction.
   [1] Casali, M. R. & Grasselli, L. 2-symmetric crystallizations and 2-fold branched coverings of S3. Discrete Math. 87, 9-22 (1991).
   [2] Cattabriga, A. & Gabrovsek, B. A Markov theorem for generalized plat decomposition. Ann. Sc. Norm. Super. Pisa Cl. Sci. XX, 1273-1294 (2018).
   
   
9. LabAGTA Seminar: Paolo Cavicchioli (University of Modena), March 24, 2022, 11:30-12:30.
   Title: Plat closure of braids in E^3.
   Abstract: In this seminar, we will define what a plat closure of braid is, describe its main properties and its relation to Hilden groups. In the second part of the seminar we will answer to the problem of passing from the plat form of a braid to the standard one and vice versa.