Analysis-seminar May 2024

analysis-seminar@lists.dm.unipi.it

1 participants
3 discussions

Reminder seminari domani (9 maggio)
by Ilaria Lucardesi 08 May '24

08 May '24

Care tutte, cari tutti, vi ricordiamo il seminario di domani: Annalisa Massaccesi (Università di Padova),<https://www.dm.unipi.it/en/seminar/?id=662981ff25ce23c048c43fb8> alle ore 17 (+ merenda alle 16:45), in Aula Magna. A presto, Ilaria Lucardesi e Luigi Forcella --------------------------------------------- Dear all, we remind you of the seminar of tomorrow: Annalisa Massaccesi (Università di Padova),<https://www.dm.unipi.it/en/seminar/?id=662981ff25ce23c048c43fb8> at 5PM (+ snack at 4:45PM), Aula Magna. See you soon, Ilaria Lucardesi and Luigi Forcella

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Annuncio seminario 9 maggio
by Ilaria Lucardesi 03 May '24

03 May '24

Care tutte, cari tutti, per il prossimo evento del ciclo dei Seminari di Analisi, giovedì 9 maggio alle ore 17:00, in Aula Riunioni, avremo il piacere di ascoltare Annalisa Massaccesi (Università di Padova), che terrà un seminario <https://www.dm.unipi.it/seminario/?id=662981ff25ce23c048c43fb8> <https://www.dm.unipi.it/en/seminar/?id=6618fe5c282479bbfbbfe2a2> dal titolo “Recent developments on the Besicovitch's 1/2 problem ”. Trovate qui sotto l’abstract. Il seminario sarà preceduto da una merenda dalle ore 16:45 nella stessa aula. A presto, Ilaria Lucardesi e Luigi Forcella --------------------------------------------- Dear all, On Thursday May 9th at 5PM, in "Aula Riunioni", for the Mathematical Analysis Seminar, we will have the pleasure of listening to Annalisa Massaccesi (Università di Padova). The title of the talk <https://www.dm.unipi.it/seminario/?id=662981ff25ce23c048c43fb8> <https://www.dm.unipi.it/en/seminar/?id=65a3e6d89ddab435806cde2c> <https://www.dm.unipi.it/en/seminar/?id=6618fe5c282479bbfbbfe2a2> is “Recent developments on the Besicovitch's 1/2 problem ”. Please find below the abstract. The seminar will be preceded by a snack in the same room, starting at 4:45 PM. See you soon, Ilaria Lucardesi and Luigi Forcella --------------------------------------------- Speaker: Annalisa Massaccesi (Università di Padova) Title: Recent developments on the Besicovitch's 1/2 problem Abstract: The Besicovitch's 1/2 problem problem investigates the smallest threshold 𝜎 guaranteeing rectifiability for a set with Hausdorff 1-dimensional finite measure when the lower density of the set is larger than 𝜎 almost everywhere. Besicovitch conjectured that 𝜎 = 1/2 (hence the name of the problem) and proved 𝜎 ≤ 3/4, then Preiss and Tišer improved the bound to 𝜎≤ (2+\sqrt{46})/12 ∼ 0.73186... In a recent work in collaboration with C. De Lellis, F. Glaudo and D. Vittone, we devised a strategy to improve the bound by means of a hierarchy of variational problems and we reach a proof that 𝜎≤0.7. In this seminar, I will try to explain the fairly intuitive geometric idea behind this strategy and I will try to summarize both the computational obstacles and the intrinsic obstacles that are still in the way.

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Annuncio seminari 29 aprile e 2 maggio
by Ilaria Lucardesi 02 May '24

02 May '24

Care tutte, cari tutti, la prossima settimana avremo due seminari di Analisi: lunedì 29 aprile, alle ore 17:30 (+ merenda post-seminario) in aula seminari, avremo il piacere di ascoltare Luca Lussardi (Polito), che terrà un seminario <https://www.dm.unipi.it/en/seminar/?id=66013124282479bbfbbaaac1> dal titolo “Nematic soap films”; giovedì 2 maggio, alle ore 17 (+ merenda alle 16:45), in aula riunioni, avremo il piacere di ascoltare Giacomo Del Nin (Max-Planck-Institut, Lipsia), che terrà un seminario <https://www.dm.unipi.it/en/seminar/?id=662778461ab535c3c8d5fa0c> dai titolo "BMO-type seminorms and local Poincaré constants for BV functions". Trovate qui sotto i due abstract. A presto, Ilaria Lucardesi e Luigi Forcella --------------------------------------------- Dear all, next week, for the Mathematical Analysis Seminar, there will be two seminars: on Monday 29th April at 5:30PM (+ snack after the seminar), in "Aula Seminari", we will have the pleasure of listening to Luca Lussardi (PoliTo). The title of the talk <https://www.dm.unipi.it/en/seminar/?id=66013124282479bbfbbaaac1> <https://www.dm.unipi.it/en/seminar/?id=6602fa9a282479bbfbbb1ff6> <https://www.dm.unipi.it/en/seminar/?id=66013124282479bbfbbaaac1> is "Nematic soap films"; on Thursday 2nd May at 5PM (+ snack at 4:45PM), in "Aula Riunioni", we will have the pleasure of listening to Giacomo Del Nin (Max-Planck-Institut, Leipzig) . The title of the talk<https://www.dm.unipi.it/en/seminar/?id=662778461ab535c3c8d5fa0c> <https://www.dm.unipi.it/en/seminar/?id=6617a944282479bbfbbf84a2> <https://www.dm.unipi.it/en/seminar/?id=662778461ab535c3c8d5fa0c> is "BMO-type seminorms and local Poincaré constants for BV functions". Please find below the abstracts. See you soon, Ilaria Lucardesi and Luigi Forcella --------------------------------------------- Speaker: Luca Lussardi (PoliTo) Title: Nematic soap films Abstract: Nematic films are thin fluid structures, ideally two dimensional, endowed with an in-plane degenerate nematic order. Some variational models for nematic films have been introduced by Giomi in 2012 and by Napoli and Vergori in 2018. At equilibrium, the shape of the nematic film results from the competition between surface tension, which favors the minimization of the area, and the nematic elasticity, which instead promotes the alignment of the molecules along a common direction. The main difference between the two mentioned approaches is the way to compute the surface derivative of the nematic vector field. In this seminar I will briefly describe the models and I will present some recent analytical results obtained in collaboration with Giulia Bevilacqua, Chiara Lonati and Alfredo Marzocchi. Speaker: Giacomo Del Nin (Max-Planck-Institut, Lipsia) Title: BMO-type seminorms and local Poincaré constants for BV functions Abstract: In 2015 Bourgain, Brezis, and Mironescu introduced a class of BMO-type functionals that measure the oscillation of a function on a family of disjoint ϵ-cubes. These functionals turned out to be related to the total variation of the function, and over the years several authors have addressed the problem of finding an expression for their limit as ϵ goes to zero. Thanks to the work of many, we now know that for SBV functions the limit exists and coincides with 1/2 times the jump variation plus 1/4 times the absolutely continuous variation. However, for BV functions with a non-trivial Cantor part, the limit might not exist. In this talk I will present a natural relaxation of these functionals that enforces the existence of the limit for any BV function. I will show that this limit is related to a quantity that we introduce, the local Poincarè constant of the function, and I will discuss some challenging open questions. This result is based on a project with Adolfo Arroyo-Rabasa (Bonn) and Paolo Bonicatto (Trento).

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Analysis-seminar May 2024