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Welcome to the Department of Mathematics

What's Happening This Week In Mathematics....

 

CSC Weekly Seminar
Friday, January 23, 2015
2:30 pm
TASC-2, Rm 8500

Speaker : Jan Bouwe van den Berg (VU University Amsterdam)

Title: Validated Computations in ODEs and PDEs

Abstract: We often simulate dynamics on a computer, or calculate a numerical solution to
a partial differential equation. This gives very detailed, stimulating
information. However, it would be even better if we can be sure that what we
see on the screen genuinely represents a solution of the problem. In
particular, rigorous validation of the computations would allow such objects to
be used as ingredients of theorems. The past few decades have seen enormous
advances in the development of computer assisted proofs in dynamics. Attention
is now turning to infinite dimensional nonlinear dynamics generated by PDEs,
integral equations, delay equations, and infinite dimensional maps. In this
talk we will review recent developments, such as connecting orbit problems in
pattern formation, as well as applications in the setting of spatio-temporal
periodicity.

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Upcoming Events

  • PIMS Distinguished lecture; lunch provided
    12:30 PM - 2:30 PM
    January 27, 2015
    Speaker: Michael Singer (NCSU) (PIMS Distinguished Visitor) Location: Irmacs Title: Differential Groups and the Gamma Function PROGRAM: 12:30 - 1:29 Lunch Reception at IRMACS 1:30 - 2:20 Presentation Abstract: In 1887, Hoelder proved that the Gamma Function, defined by the difference equation y(x+1) = x y(x), satisfies no nonzero polynomial differential equation with complex coefficients. In the last several years Galois theories have been developed that reprove this result and allow one to characterize when functions satisfying certain linear differential or difference equations also satisfy auxiliary difference or differential equations. These Galois theories allow one to reduce such kinds of questions to questions concerning linear differential or difference groups, that is groups of matrices whose entries are functions satisfying a fixed set of differential or difference equations. I will give an introduction to the theory of these groups and the related Galois theories and survey recent results applying these theories to questions of functional transcendence.
  • SFU/UBC Number Theory Seminar
    3:30 PM - 4:30 PM
    January 29, 2015
    Speaker: Nils Bruin (SFU) Title: Genus 2 curves with (3, 3)-isogenies and 3-torsion in Sha Abstract: We parametrize genus 2 curves with a maximal isotropic (Z/3)^2 in their Jacobian, together with an explicit description of the associated isogeny. This allows us to perform (3, 3)-isogeny descent on various simple principally polarized abelian surfaces and exhibit non-trivial 3-part in their Tate-Shafarevich groups. This is joint work with Victor Flynn and Damiano Testa.
  • Discrete Math Seminar: Manuel Kauers
    1:30 PM - 2:30 PM
    February 3, 2015
    Tuesday February 3, 1:30PM k9509 Speaker: Manuel Kauers (RISC) Title:Walks in the Quarter Plane with Multiple Steps
  • Discrete Math Seminar
    1:30 PM - 2:30 PM
    February 3, 2015
    No Description
  • Operations Research Seminar: Soon-Yi Wu
    2:30 PM - 3:30 PM
    February 5, 2015
    Title: On finite convergence of an explicit exchange method for convex semi-infinite programming problems with second-order cone constraints Abstract: In this talk, we propose an explicit exchange algorithm for solving semi-infinite programming problem (SIP) with second-order cone (SOC) constraints. We prove, by using the slackness complementarity conditions, that the algorithm terminates in a finite number of iterations and the obtained solution sufficiently approximates the original SIP solution. In existing studies on SIPs, only the nonnegative constraints were considered, and hence, the slackness complementarity conditions were separable to each component. However, in our study, the existing componentwise analyses are not applicable anymore since the slackness complementarity conditions are associated with SOCs. In order to overcome such a difficulty, we introduce a certain coordinate system based on the spectral factorization. In the numerical experiments, we solve some test problems to see the effectiveness of the proposed algorithm.
  • Discrete Math Seminar
    1:30 PM - 2:30 PM
    February 17, 2015
    No Description
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