Tue, 31 Mar 2020
14:00
Virtual

Erdős covering systems

Rob Morris
(IMPA)
Further Information

This is the first instalment of the new Oxford Discrete Maths and Probability seminar, held via Zoom. Please see the main seminar site here for further details.

Links: slides and video recording (to come)

Abstract

A covering system of the integers is a finite collection of arithmetic progressions whose union is the set of integers $\mathbb{Z}$. The study of these objects was initiated in 1950 by Erdős, and over the following decades he asked a number of beautiful questions about them. Most famously, his so-called 'minimum modulus problem' was resolved in 2015 by Hough, who proved that in every covering system with distinct moduli, the minimum modulus is at most $10^{16}$.

In this talk I will describe a simple and general method of attacking covering problems that was inspired by Hough's proof. We expect that this technique, which we call the 'distortion method', will have further applications in combinatorics.

This talk is based on joint work with Paul Balister, Béla Bollobás, Julian Sahasrabudhe and Marius Tiba.

The Coronavirus disease pandemic (COVID-19) poses unprecedented challenges for governments and societies around the world. In addition to medical measures, non-pharmaceutical measures have proven to be critical for delaying and containing the spread of the virus. However, effective and rapid decision-making during all stages of the pandemic requires reliable and timely data not only about infections, but also about human behaviour, especially on mobility and physical co-presence of people. 

Thu, 02 Apr 2020
16:00

What is the Jiang Su algebra (Virtual Seminar)

Sam Evington
(University of Oxford)
Further Information

This is the first meeting of the virtual operator algebra seminar in collaboration with colleagues in Glasgow and UCLan.  The seminar will take place by zoom, and the meeting details will be available here.

Cosmological inference from within the peculiar local universe
Mohayaee, R Rameez, M Sarkar, S (23 Mar 2020)
Combined search for neutrinos from dark matter self-annihilation in the
Galactic Centre with ANTARES and IceCube
Collaboration, A Albert, A André, M Anghinolfi, M Ardid, M Aubert, J Aublin, J Baret, B Basa, S Belhorma, B Bertin, V Biagi, S Bissinger, M Boumaaza, J Bouta, M Bouwhuis, M Brânzaş, H Bruijn, R Brunner, J Busto, J Capone, A Caramete, L Carr, J Celli, S Chabab, M Chau, T Moursli, R Chiarusi, T Circella, M Coleiro, A Colomer, M Coniglione, R Coyle, P Creusot, A Díaz, A Deschamps, A Distefano, C Palma, I Domi, A Donzaud, C Dornic, D Drouhin, D Eberl, T Khayati, N Enzenhöfer, A Ettahiri, A Fermani, P Ferrara, G Filippini, F Fusco, L Gay, P Glotin, H Gozzini, R Ruiz, R Graf, K Guidi, C Hallmann, S Haren, H Heijboer, A Hello, Y Hernández-Rey, J Hößl, J Hofestädt, J Huang, F Illuminati, G James, C Jong, M Jong, P Jongen, M Kadler, M Kalekin, O Katz, U Khan-Chowdhury, N Kouchner, A Kreykenbohm, I Kulikovskiy, V Lahmann, R Breton, R Lefèvre, D Leonora, E Levi, G Lincetto, M Lopez-Coto, D Loucatos, S Maggi, G Manczak, J Marcelin, M Margiotta, A Marinelli, A Martínez-Mora, J Mele, R Melis, K 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Executive stock options (ESOs) are contracts awarded to employees of companies, which confer the right to reap the profit from buying the company stock (exercising the ESO) at or before a fixed maturity time $T$, for a fixed price specified in the contract (the strike price of the ESO). ESOs are used to augment the remuneration package of employees, the idea being to give them an incentive to boost the company's fortunes, and thus the stock price, making their ESO more valuable.

Social distancing measures to reduce the spread of the novel coronavirus are in place worldwide. These guideline are for everyone. We are all expected to reduce our contact with others, and this will have some negative impacts in terms of mental health and loneliness, particularly for the elderly and other vulnerable groups. So why should we follow measures that seem so extreme? The answer is simple. Social distancing works. It reduces transmission of the virus effectively and lessens the impact on already stretched healthcare services.

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