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SUMMARY:NBIA Algebra Day
DTSTART:20260915T070000Z
DTEND:20260915T140000Z
DTSTAMP:20260921T081600Z
UID:indico-event-2300@indico.nbi.ku.dk
DESCRIPTION:\nAlgebra sits at the crossroads of mathematics and physics 
 — a shared language that appears many places and often allows tackling c
 omputations. The NBIA Algebra Day will bring together mathematicians and p
 hysicists for a day of talks exploring this common ground\, held in the hi
 storical Auditorium A of the Niels Bohr Institute on Blegdamsvej. The talk
 s this year will cover a range of topics\, from classical questions about 
 systems of linear equations in polynomials to the algebra behind deformati
 ons of shapes. \nAll participants are invited for lunch at Restaurant Po
 st \nTimetable:\n9:45 Coffee\, tea\, and pastries\n10-10:45 David Eisenbu
 d\n10:45-11 Coffee break\n11-11:45 Elisenda Feliu\n12-13:30 lunch at Resta
 urant Post\n13:30-14:00 Emil Bjerrum-Bohr: History of Niels Bohr Institute
 \n14:00-14:45 Nathalie Wahl\nTalk titles and abstracts:\nSpeaker: David Ei
 senbud\nTitle: Linear Equations in polynomials. \n \nAbstract: Given pol
 ynomials $a_1\,...\,a_n$  with complex coefficients\, in $d$ variables\, 
 what can you say about  the solutions of the equation $\\sum_{i=1}^n a_i(
 x) f_i = 0$ ? Here the task is to find enough vectors $F^j := (f_1^j\, f_2
 \, ...\, f_n^j)$ of polynomials solving the equation so that every vector
   $G = (g_1\,...\,g_n)$ of polynomials solving the equation can be writte
 n in the form $G = \\sum_j h_j(x) F^j$ for some polynomials $h_j(x)$. If t
 he $F^j\, G$\, and the  $h_j$ were allowed to be rational functions\, thi
 s problem would look like standard linear algebra\; the difficulty is that
  the quotient of two polynomials\, such as $x/y$\,  isn't usually a polyn
 omial. Understanding how to think about this problem was part of what Davi
 d Hilbert did around 1890 in the course of solving the main problems of  
 the invariant theory of the time. In this overview talk I'll describe what
  Hilbert did\, and why\, and show some of the modern developments in the t
 heory.\n \nSpeaker: Elisenda Feliu\n \nTitle: Algebra and reaction netwo
 rks.\n \nAbstract: Biochemical reaction networks describe how interacting
  (bio)chemical species evolve over time. Their dynamics are commonly model
 led by systems of ordinary differential equations whose right-hand sides a
 re polynomial or rational functions. Fundamental questions include whether
  a network can admit multiple equilibria\, whether these equilibria are st
 able\, and how qualitative changes in the dynamics (bifurcations) can occu
 r as parameters vary. Many of these questions can be reformulated as probl
 ems about the solutions of systems of polynomial equations and inequalitie
 s\, making them amenable to methods from algebra and real algebraic geomet
 ry. This talk will introduce the mathematical framework of reaction networ
 ks and illustrate how algebraic techniques can be used to study several as
 pects of their dynamics.\n \n\n \n \nSpeaker: Nathalie Wahl\n \n\nTitl
 e: When are two shapes really the same?\nAbstract: Two topological spaces 
 are "the same" (homeomorphic) if there is a continuous map with continuous
  inverse relating them\, while they are homotopic if one can be deformed i
 nto the other. Whitehead torsion is an algebraic invariant that\, in some 
 sense\, measures how far a homotopy equivalence is from being a homeomorph
 ism. The talk will introduce this invariant\, and explain how studying the
  behavior of strings in manifolds lead to the definition of a geometric sh
 adow of this invariant in the world of manifolds.\n\n \n \nOrganizers: D
 avid Eisenbud\, Nathalie Wahl\, and Poul H. Damgaard\n\nhttps://indico.nbi
 .ku.dk/event/2300/
URL:https://indico.nbi.ku.dk/event/2300/
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