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The thesis, with the title of Vector bundles and sheaves on toric varieties, has been supervised by Rosa Maria Miró Roig, professor at the Universitat de Barcelona and CRM researcher.

Martí obtained a Bachelor degree in Mathematics in 2017, and finished a Master degree in Advanced Mathematics in 2019, both degrees at the Universitat de Barcelona. He has completed his PhD project enrolled at the program in Mathematics at the UB, supported by a FPI grant from CRM-BGSmath. His research focused on the study of vector bundles on algebraic varieties and its interactions with combinatorics and commutative algebra.

On behalf of all CRM members, we would like to wish Martí the best of luck in his upcoming thesis defense.

CRM Comm Team

CRM Comm Team

Anna Drou | Pau Varela

CRMComm@crm.cat

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Fish schools and growing tissues: a workshop on how collective behaviour emerges

Fish schools and growing tissues: a workshop on how collective behaviour emerges

The Centre de Recerca Matemàtica (CRM) organised the Barcelona Workshop on Kinetic and Macroscopic Models in Biology with Friends II, held from 7 to 10 September at the Institut d’Estudis Catalans. More than thirty researchers discussed how order at the scale of tissues and animal groups arises from local interactions between individuals, in a programme that included talks by CRM researchers Daria Stepanova and Juan Arellano-Tintó. Two of the speakers, James Sharpe (EMBL Barcelona) and Chiara Villa (CNRS, Université Paris Cité), talked to the CRM about their research.

Almost every automaton can be reset with a short word

Almost every automaton can be reset with a short word

Guillaume Chapuy (Université Paris Cité, CNRS) and Guillem Perarnau (UPC, CRM) have shown that a random finite automaton with n states can, with high probability, be reset by a word of length of order √n log n. The result, published in ACM Transactions on Algorithms, pins the exponent at 1/2, the lower end of a decade of numerical estimates, and addresses the random version of the synchronization problem behind a conjecture Ján Černý posed in 1964 and which still remains open.