Kalle Karu


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Graduate Student Supervision

Master's Student Supervision (2010 - 2018)
Moduli Space of Sheaves on Fans (2011)

A conjecture of H. Hopf states that if x(M²n) is a closed, Riemannian manifold of nonpositive sectional curvature, then its Euler characteristic x(M²n), should satify (-1)n x(M²n)≥ 0. Ruth Charney and Michael Davis investigated the conjecture in the context of piecewise Euclidean manifolds having "nonpositive curvature" in the sense of Gromov's CAT(0) inequality. In that context the conjecture can be reduced to a local version which predicts the sign of a "local Euler characteristic" at each vertex. They stated precisely various conjectures in their paper which we are interested in one of them stated as Conjecture D (see [1]) which is equivalent to the Hopf Conjecture for piecewise Euclidean manifolds cellulated by cubes.The goal of this thesis is to study the Charney - Davis Conjecture stated as Conjecture (D) by using sheaves on fans.

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Faculty of Science Information Session

Date: Tuesday, 24 November 2020
Time: 10:00 to 11:00
UBC’s Faculty of Science is home to an array of outstanding scientists and students who strive to unravel the principles that underlie our universe - from the subatomic to the macroscopic, from pure mathematics to biotechnology, from ecosystems to galactic systems. In this session hosted by Professor Mark MacLachlan, Associate Dean of Research & Graduate Studies, we’ll hear from faculty members and graduate students on some of the exciting research happening within the Faculty of Science. We’ll also take a look at the wide range of graduate programs available, what its like to be a grad student in Science, and also provide some application advice. Be sure to join us and get an insight into how UBC Science is discovering new scientific knowledge and preparing Canada’s and the world’s next generation of scientists.

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