Guest lectures and seminars - Page 3
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Erling Svedrups plass and Zoom https://uio.zoom.us/j/66503159220?pwd=alhPVFpHNUxVUTNoeHhIcVFtUWx4UT09
In this talk I will cover the recent advances in the theory of power law distributions, in particular the role of Markov modulation and random stopping emphasized by Beare and Toda (2022), which builds on Nakagawa (2007)’s Tauberian theorem. Applications include the emergence of Zipf’s law in Japanese cities and the spread of COVID-19. I will also present open mathematical problems.
• Beare, Brendan K., and Alexis Akira Toda. "Determination of Pareto exponents in economic models driven by Markov multiplicative processes." Econometrica 90.4 (2022): 1811-1833.
• Nakagawa, Kenji. "Application of Tauberian theorem to the exponential decay of the tail probability of a random variable." IEEE Transactions on Information Theory 53.9 (2007): 3239-3249.
• Beare, Brendan K., and Alexis Akira Toda. "On the emergence of a power law in the distribution of COVID-19 cases." Physica D: Nonlinear Phenomena 412 (2020): 132649.
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NHA 107
C*-algebra seminar by Eduard Vilalta (Chalmers University of Technology / University of Gothenburg)
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QOMBINE seminar talk by Franz Fuchs (University of Oslo)
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NHA B1120
Donaldson-Thomas invariants "virtually" count curves in a given threefold. They factor into two parts: a part which only counts curves, and a degree 0 part, which counts 0-dimensional subschemes. The degree 0 part can be fully computed with a closed formula by relating them to combinatorial counting of plane partitions, which are certain configurations of boxes in 3D space. DT theory comes in various refinements. Nekrasov's formula refines the relation to counts of plane partitions to equivariant K-theoretic DT theory and gives a closed formula for refined degree 0 DT invariants.
Degree 0 DT invariants of orbifolds are related to counts of colored plane partitions, where the boxes are colored in a way determined by the orbifold structure. This allows the computation of closed formulas for some orbifolds. We refine these closed formulas to equivariant K-theoretic DT theory by modifying the techniques used in Okounkov's proof of Nekrasov's formula to work for orbifolds. We will explain these techniques in the case of schemes and describe some of the modifications to make them work for orbifolds.