IA Scholar Query: Maximal intersecting families and affine regular polygons in PG(2, q).
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgThu, 22 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Hurwitz numbers for reflection groups II: Parabolic quasi-Coxeter elements
https://scholar.archive.org/work/glpyk7qqivcbnibclqlfhmkbyq
We define parabolic quasi-Coxeter elements in well generated complex reflection groups. We characterize them in multiple natural ways, and we study two combinatorial objects associated with them: the collections Red_W(g) of reduced reflection factorizations of g and RGS(W,g) of the relative generating sets of g. We compute the cardinalities of these sets for large families of parabolic quasi-Coxeter elements and, in particular, we relate the size #Red_W(g) with geometric invariants of Frobenius manifolds. This paper is second in a series of three; we will rely on many of its results in part III to prove uniform formulas that enumerate full reflection factorizations of parabolic quasi-Coxeter elements, generalizing the genus-0 Hurwitz numbers.Theo Douvropoulos, Joel Brewster Lewis, Alejandro H. Moraleswork_glpyk7qqivcbnibclqlfhmkbyqThu, 22 Sep 2022 00:00:00 GMTThe basolateral amygdala-anterior cingulate pathway contributes to depression and its comorbidity with chronic pain
https://scholar.archive.org/work/2huqwxjlgzewhaggyjan5764ui
AbstractWhile depression and chronic pain are frequently comorbid, underlying neuronal circuits, and their relevance for the understanding of psychopathology, remain poorly defined. Here we show in mice that hyperactivity of the neuronal pathway linking the basolateral amygdala to the anterior cingulate cortex is essential for chronic pain-induced depression. In naive animals, we demonstrate that activation of this pathway is sufficient to trigger depressive-like behaviors, as well as transcriptomic alterations that recapitulate core molecular features of depression in the human brain. These alterations notably impact gene modules related to myelination and the oligodendrocyte lineage. Among these, we show that Sema4a, a hub gene significantly upregulated in both mice and humans in the context of altered mood, is necessary for the emergence of depressive-like behaviors. Overall, these results place the BLA-ACC pathway at the core of pain and depression comorbidity, and unravel the role of impaired myelination and Sema4a in mood control.Léa J Becker, Clémentine Fillinger, Robin Waegaert, Pierre Hener, Beyza Ayazgok, Muris Humo, Sarah H Journée, Meltem Karatas, Laetitia Degiorgis, Marie des Neiges Santin, Mary Mondino, Michel Barrot, El Chérif Ibrahim, Gustavo Turecki, Raoul Belzeaux, Pierre Veinante, Laura A Harsan, Sylvain Hugel, Pierre-Eric Lutz, Ipek Yalcinwork_2huqwxjlgzewhaggyjan5764uiThu, 11 Aug 2022 00:00:00 GMTSimple fibrations in (1,2)-surfaces
https://scholar.archive.org/work/de5lyzfx3feb3ctv6yym3r43z4
We introduce the notion of a simple fibration in (1,2)-surfaces. That is, a hypersurface inside a certain weighted projective space bundle over a curve such that the general fibre is a minimal surface of general type with p_g=2 and K^2=1. We prove that almost all Gorenstein simple fibrations over the projective line with at worst canonical singularities are canonical threefolds "on the Noether line" with K^3=4/3 p_g-10/3, and we classify them. Among them, we find all the canonical threefolds on the Noether line that have previously appeared in the literature. The Gorenstein simple fibrations over ℙ^1 are Cartier divisors in a toric 4-fold. This allows to us to show among other things, that the previously known canonical threefolds on the Noether line form an open subset of the moduli space of canonical threefolds, that the general element of this component is a Mori Dream Space, and that there is a second component when the geometric genus is congruent to 6 modulo 8; the threefolds in this component are new.Stephen Coughlan, Roberto Pignatelliwork_de5lyzfx3feb3ctv6yym3r43z4Thu, 14 Jul 2022 00:00:00 GMTEnhancing the use of scenario-based biodiversity information in conservation policy and practice
https://scholar.archive.org/work/xveoszbqo5cr7evcl73xhxsocu
Diese Dissertation zielt darauf ab, die Nutzung szenariobasierter Biodiversitätsinformationen in der Naturschutzpolitik und -praxis zu verbessern. Zunächst untersuche ich die Auswirkungen des Klimawandels und der Landnutzung auf die biologische Vielfalt und die Ökosystemleistungen durch einen Modellvergleich. Dann entwickle und beschreibe ich einen neuen Szenariorahmen "Nature Futures Framework" mit seinem methodischen Leitfaden für die Modellierung von Nature Futures Szenarien. Abschließend führe ich eine retrospektive Analyse von Schutzgebieten durch die "Nature Futures"-Linse unter Verwendung wesentlicher Variablen durch. In dieser Dissertation wird vorgeschlagen, Klima- und Biodiversitätsforschungsgemeinschaften bei der Entwicklung von Nachhaltigkeitsszenarien zusammenzubringen. Sie fördert die Integration verschiedener Werte und Weltanschauungen in Szenarien, um breitere gesellschaftliche Interessengruppen in die Erreichung nachhaltiger Zukünfte einzubinden. Sie schlägt vor, wissenschaftliche und politische Rahmenwerke bei der Umsetzung von Schutz- und Nachhaltigkeitszielen miteinander zu verweben.HyeJin Kim, Universitäts- Und Landesbibliothek Sachsen-Anhalt, Martin-Luther Universität, Henrique M. Pereira, Christine Fürst, Patricia Balvanerawork_xveoszbqo5cr7evcl73xhxsocuFri, 17 Jun 2022 00:00:00 GMTLocality of relative symplectic cohomology for complete embeddings
https://scholar.archive.org/work/lqgv3wqga5g3pe46mvpq6xtkeq
A complete embedding is a symplectic embedding ι:Y→ M of a geometrically bounded symplectic manifold Y into another geometrically bounded symplectic manifold M of the same dimension. When Y satisfies an additional finiteness hypothesis, we prove that the truncated relative symplectic cohomology of a compact subset K inside Y is naturally isomorphic to that of its image ι(K) inside M. Under the assumption that the torsion exponents of K are bounded we deduce the same result for relative symplectic cohomology. We introduce a technique for constructing complete embeddings using what we refer to as integrable anti-surgery. We apply these to study symplectic topology and mirror symmetry of symplectic cluster manifolds and other examples of symplectic manifolds with singular Lagrangian torus fibrations satisfying certain completeness conditions.Yoel Groman, Umut Varolguneswork_lqgv3wqga5g3pe46mvpq6xtkeqWed, 15 Jun 2022 00:00:00 GMTGeneralized Quadrangles Of Order (s, s^2). IV. Translations, Moufang And Fong-Seitz
https://scholar.archive.org/work/e3ftbldjfvehpfvgqkjgt25lxa
In the period 1994-1999 Thas wrote a series of three papers on generalized quadrangles of order (s, s^2). In this Part IV we classify all finite translation generalized quadrangles of order (s, s^2) having a kernel of size at least 3, containing a regular line not incident with the translation point. There are several applications on generalized quadrangles of order (s, s^2) having at least 2 translation points, on Moufang quadrangles, and concerning the theorem of Fong and Seitz classifying all groups with a BN-pair of rank 2.Joseph A. Thaswork_e3ftbldjfvehpfvgqkjgt25lxaMon, 30 May 2022 00:00:00 GMTLangevin dynamic for the 2D Yang-Mills measure
https://scholar.archive.org/work/i2dj7wkck5dxrhqgqn4qbl5uru
We define a natural state space and Markov process associated to the stochastic Yang-Mills heat flow in two dimensions. To accomplish this we first introduce a space of distributional connections for which holonomies along sufficiently regular curves (Wilson loop observables) and the action of an associated group of gauge transformations are both well-defined and satisfy good continuity properties. The desired state space is obtained as the corresponding space of orbits under this group action and is shown to be a Polish space when equipped with a natural Hausdorff metric. To construct the Markov process we show that the stochastic Yang-Mills heat flow takes values in our space of connections and use the "DeTurck trick" of introducing a time dependent gauge transformation to show invariance, in law, of the solution under gauge transformations. Our main tool for solving for the Yang-Mills heat flow is the theory of regularity structures and along the way we also develop a "basis-free" framework for applying the theory of regularity structures in the context of vector-valued noise - this provides a conceptual framework for interpreting several previous constructions and we expect this framework to be of independent interest.Ajay Chandra, Ilya Chevyrev, Martin Hairer, Hao Shenwork_i2dj7wkck5dxrhqgqn4qbl5uruWed, 25 May 2022 00:00:00 GMTModerate-density parity-check codes from projective bundles
https://scholar.archive.org/work/3xdvg7xxz5hxfgxso5hibr44i4
New constructions for moderate-density parity-check (MDPC) codes using finite geometry are proposed. We design a parity-check matrix for the main family of binary codes as the concatenation of two matrices: the incidence matrix between points and lines of the Desarguesian projective plane and the incidence matrix between points and ovals of a projective bundle. A projective bundle is a special collection of ovals which pairwise meet in a unique point. We determine the minimum distance and the dimension of these codes, and we show that they have a natural quasi-cyclic structure. We consider alternative constructions based on an incidence matrix of a Desarguesian projective plane and compare their error-correction performance with regards to a modification of Gallager's bit-flipping decoding algorithm. In this setting, our codes have the best possible error-correction performance after one round of bit-flipping decoding given the parameters of the code's parity-check matrix.Jessica Bariffi, Sam Mattheus, Alessandro Neri, Joachim Rosenthalwork_3xdvg7xxz5hxfgxso5hibr44i4Tue, 24 May 2022 00:00:00 GMTCharacteristic cycle and wild ramification for nearby cycles of étale sheaves
https://scholar.archive.org/work/re5itx7afbdybmozymrl3rz4dm
In this article, we give a bound for the wild ramification of the monodromy action on the nearby cycles complex of a locally constant \'etale sheaf on the generic fiber of a smooth scheme over an equal characteristic trait in terms of Abbes and Saito's logarithmic ramification filtration. This provides a positive answer to the main conjecture in Isabel Leal's article "On the ramification of \'etale cohomology groups" for smooth morphisms in equal characteristic. We also study the ramification along vertical divisors of \'etale sheaves on relative curves and abelian schemes over a trait.Haoyu Hu, Jean-Baptiste Teyssierwork_re5itx7afbdybmozymrl3rz4dmTue, 26 Apr 2022 00:00:00 GMTRight ventricular biomechanics in pulmonary hypertension
https://scholar.archive.org/work/pfjw57reebhfbmovczg7xnngtu
As outcome in pulmonary hypertension is strongly associated with progressive right ventricular dysfunction, the work in this thesis seeks to determine the regional distribution of forces on the right ventricle, its geometry, and deformations subsequent to load. This thesis contributes to the understanding of how circulating biomarkers of energy metabolism and stress-response pathways are related to adverse cardiac remodelling and functional decompensation. A numerical model of the heart was used to derive a three-dimensional representation of right ventricular morphology, function and wall stress in pulmonary hypertension patients. This approach was tested by modelling the effect of pulmonary endarterectomy in patients with chronic thromboembolic disease. The relationship between the cardiac phenotype and 10 circulating metabolites, known to be associated with all-cause mortality, was assessed using mass univariate regression. Increasing afterload (mean pulmonary artery pressure) was significantly associated with hypertrophy of the right ventricular inlet and dilatation, indicative of global eccentric remodelling, and decreased systolic excursion. Right ventricular ejection fraction was found to be negatively associated with 3-hydroxy-3-methylglutarate, N-formylmethionine, and fumarate. Wall stress was related to all-cause mortality and its decrease after pulmonary endarterectomy was associated with a fall in brain natriuretic peptide. Six metabolites were associated with elevated end-systolic wall stress: dehydroepiandrosterone sulfate, N2,N2-dimethylguanosine, N1-methylinosine, 3-hydroxy-3-methylglutarate, N-acetylmethionine, and N-formylmethionine. Metabolic profiles related to energy metabolism and stress-response are associated with elevations in right ventricular end-systolic wall stress that have prognostic significance in pulmonary hypertension patients. These results show that statistical parametric mapping can give regional information on the right ventricle and that metabolic phenotyping, as well as pr [...]Mark Ivan Attard, Martin Wilkins, Wellcome Trust (London, England), GlaxoSmithKlinework_pfjw57reebhfbmovczg7xnngtuMon, 21 Mar 2022 00:00:00 GMTShortest Minkowski billiard trajectories on convex bodies
https://scholar.archive.org/work/ncmso3ymobasnjrdvem4txra5q
We rigorously investigate closed Minkowski/Finsler billiard trajectories on n-dimensional convex bodies. We outline the central properties in comparison and differentiation from the Euclidean special case and establish two main results for length-minimizing closed Minkowski/Finsler billiard trajectories: one is a regularity result, the other is of geometric nature. Building on these results, we develop an algorithm for computing length-minimizing closed Minkowski/Finsler billiard trajectories in the plane.Daniel Rudolf, Stefan Kruppwork_ncmso3ymobasnjrdvem4txra5qThu, 03 Mar 2022 00:00:00 GMTCombinatorics and Metric Geometry
https://scholar.archive.org/work/7uwgpw4xcfgrtbombpi4lcckna
This thesis consists of an introduction and seven chapters, each devoted to a different combinatorial problem. In Chapters 1 and 2, we consider the main subject of this thesis; the sharp stability of the Brunn-Minkowski inequality (BM). This celebrated theorem from the 19th century asserts that for bodies A,B $\subset$ $\mathbb{R}$$^{k}$, we have |A + B|$^{1/k}$ $\geq$ |A|$^{1/k}$ + |B|$^{1/k}$, where |$\cdot$| is the Lebesgue measure and A + B := {a + b : a $\in$ A, b $\in$ B} is the Minkowski sum. Moreover, we have equality if and only if A,B are homothetic convex sets. The stability question, studied in many papers, asks how the distance to equality in BM relates to the distance from A,B to homothetic convex sets. In particular, given Brunn-Minkowsi deficit $\delta$ := |A+B|$^{1/k}$ / |A|$^{1/k}$ + |B|$^{1/k}$ -1, and normalized volume ratio $\textit{t}$ := |A|$^{1/k}$ / |A|$^{1/k}$ + |B|$^{1/k}$, what is the best bound one can find on $\omega$ := |K$_{A}$ \ A| / |A| + |K$_{B}$ \ B| / |B|, where K$_{A}$ $\supset$ A, and K$_{B}$ $\supset$ B are homothetic convex sets of minimal size? In Chapter 2, we prove a conjecture by Figalli and Jerison establishing the sharp stability for homothetic sets. In particular, we show that for homothetic sets, we have $\omega$ = O$_{k}$($\delta$t$^{-1}$), for $\delta$ sufficiently small. In Chapter 3, we establish the sharp stability for planar sets, i.e. we show that for planar sets and $\delta$ sufficiently small, we have $\omega$ = O($\delta$$^{1/2}$t$^{-1/2}$). A crucial result in Chapter 3 shows that for any $\epsilon$ > 0, if $\delta$ is sufficiently small, then we have |co(A + B) \ (A + B)| $\leq$ (1 + $\epsilon$)(|co(A) \ A| + |co(B) \ B|). In Chapter 4, we consider a reconstruction problem for functions on graphs. Given a function $\textit{f}$:V(G) $\rightarrow$ [k] on the vertices of a graph G and a random walk (U$_{i}$)$^{{\infty}}_{i = 1}$ on that graph, can we reconstruct $\textit{f}$ (up to automorphisms) based on just ($\textit{f}$(U$_{i}$)$^{{\infty}}_{i = 1}$ [...]Peter Van Hintum, Apollo-University Of Cambridge Repository, Béla Bollobáswork_7uwgpw4xcfgrtbombpi4lccknaFri, 18 Feb 2022 00:00:00 GMTAcylindrical and strong accessibility
https://scholar.archive.org/work/pzaqfyymazcfzmrxrrmchsv4tu
Weidmann has produced a bound on the number of edges of a graph of groups splitting for when a finitely generated group acts on a tree (𝑘,𝐶)-acylindrically [25]. In the same paper Weidmann conjectures a common generalisation between their result and a theorem of Bestvina and Feighn [2]; which provides a similar bound for finitely generated groups acting on a tree with small edge stabilisers. We will produce an example which shows this conjecture is false. We then extend Weidmann's result to actions which are 𝑘-acylindrical except on some set of subgroups with finite height. We then apply this result to a couple of specific cases. The first gives us a bound for actions of hyperbolic groups which are 𝑘-acylindrical on non virtually-cyclic subgroups. The second give a bound for a RAAG acting 𝑘-acylindrically on non-abelian subgroups. We also provide a sharp bound for finitely generated groups acting 𝑘-acylindrically. We also touch on the subject of strong accessibility. In particular we give an account of a theorem by Louder and Touikan [19] which shows that many hierarchies consisting of slender JSJ-decompositions are finite; in particular JSJ-hierarchies of 2-torsion-free hyperbolic groups are always finite.Michael Hill, Apollo-University Of Cambridge Repository, Henry Wiltonwork_pzaqfyymazcfzmrxrrmchsv4tuFri, 04 Feb 2022 00:00:00 GMTProvable tradeoffs in adversarially robust classification
https://scholar.archive.org/work/cqgyh57wmje67kckho4mfgv3oq
It is well known that machine learning methods can be vulnerable to adversarially-chosen perturbations of their inputs. Despite significant progress in the area, foundational open problems remain. In this paper, we address several key questions. We derive exact and approximate Bayes-optimal robust classifiers for the important setting of two- and three-class Gaussian classification problems with arbitrary imbalance, for ℓ_2 and ℓ_∞ adversaries. In contrast to classical Bayes-optimal classifiers, determining the optimal decisions here cannot be made pointwise and new theoretical approaches are needed. We develop and leverage new tools, including recent breakthroughs from probability theory on robust isoperimetry, which, to our knowledge, have not yet been used in the area. Our results reveal fundamental tradeoffs between standard and robust accuracy that grow when data is imbalanced. We also show further results, including an analysis of classification calibration for convex losses in certain models, and finite sample rates for the robust risk.Edgar Dobriban, Hamed Hassani, David Hong, Alexander Robeywork_cqgyh57wmje67kckho4mfgv3oqSun, 30 Jan 2022 00:00:00 GMTCategorification and Dynamics in Generalised Braid Groups
https://scholar.archive.org/work/h4bl54jxwfa77cn4pbnazdcagm
Recent developments in the theory of stability conditions and its relation to Teichmuller theory have revealed a deep connection between triangulated categories and surfaces. Motivated by this, we prove a categorical analogue of the Nielsen-Thurston classification theorem for the rank two generalised braid groups by viewing them as (sub)groups of autoequivalences of certain triangulated categories. This can be seen as a (categorical) generalisation of the classification known for the type A braid groups when viewed as mapping class groups of the punctured discs. Firstly, we realise the generalised braid groups as groups of autoequivalences through categorical actions that categorify the corresponding Burau representations. These categorifications are achieved by constructing certain algebra objects in the tensor categories associated to the quantum group sl2, generalising the construction of zigzag algebras used in the categorical actions of simply-laced-type braid groups to include the non-simply-laced-types. By viewing the elements of the generalised braid groups as autoequivalences of triangulated categories, we study their dynamics through mass growth (categorical entropy), as introduced by Dimitrov-Haiden-Katzarkov-Kontsevich. Our classification is then achieved in a similar fashion to Bestvina-Handel's approach to the Nielsen-Thurston classification for mapping class groups. Namely, our classification can be effectively decided through a given algorithm that also computes the mass growth of the group elements. Moreover, it shows that the mass growth of the pseudo-Anosov elements are computable from certain rank two matrices.Edmund Heng, University, The Australian Nationalwork_h4bl54jxwfa77cn4pbnazdcagmSun, 23 Jan 2022 00:00:00 GMTGraphs and complexes of lattices
https://scholar.archive.org/work/ylrj5eg2lfgtnkfwtvmzhfzstm
We study lattices acting on CAT(0) spaces via their commensurated subgroups. To do this we introduce the notions of a graph of lattices and a complex of lattices giving graph and complex of group splittings of CAT(0) lattices. Using this framework we characterise irreducible uniform (Isom(𝔼^n)× T)-lattices by C^∗-simplicity and give a necessary condition for lattices in products with a Euclidean factor to be biautomatic. We also construct non-residually finite uniform lattices acting on arbitrary products of right-angled buildings and non-biautomatic lattices acting on the product of 𝔼^n and a right-angled building.Sam Hugheswork_ylrj5eg2lfgtnkfwtvmzhfzstmMon, 17 Jan 2022 00:00:00 GMTThe symplectic geometry of surface group representations in genus zero
https://scholar.archive.org/work/mx2hvhlo25ftbbnlmcutlxd6ey
We study a compact family of totally elliptic representations of the fundamental group of a punctured sphere into PSLp2, Rq discovered by Deroin and Tholozan and named after them. We describe a polygonal model that parametrizes the relative character variety of Deroin-Tholozan representations in terms of chains of triangles in the hyperbolic plane. We extract action-angle coordinates from our polygonal model as geometric quantities associated to chains of triangles. The coordinates give an explicit isomorphism between the space of representations and the complex projective space. We prove that they are almost global Darboux coordinates for the Goldman symplectic form. This work also investigates the dynamics of the mapping class group action on the relative character variety of Deroin-Tholozan representations. We apply symplectic methods developed by Goldman and Xia to prove that the action is ergodic. vii Zusammenfassung Wir untersuchen eine kompakte Familie von total elliptischen Darstellungen der Fundamentalgruppe einer punktierten Sphäre in PSLp2, Rq, die von Deroin und Tholozan entdeckt und nach ihnen benannt wurde. Wir beschreiben ein polygonales Modell, das die relative Charaktervarietät der Deroin-Tholozan-Darstellungen in Form von Ketten von Dreiecken in der hyperbolischen Ebene parametrisiert. Wir extrahieren Wirkungs-Winkelkoordinaten aus unserem polygonalen Modell als geometrische Größen, die mit Dreiecksketten assoziiert sind. Die Koordinaten ergeben einen expliziten Isomorphismus zwischen dem Raum der Darstellungen und dem komplexen projektiven Raum. Wir beweisen, dass sie fast globale Darboux-Koordinaten für die symplektische Goldman-Form sind. In dieser Arbeit wird auch die Dynamik der Wirkung der Abbildungsklassengruppe auf der relativen Charaktervarietät von Deroin-Tholozan-Darstellungen untersucht. Wir wenden symplektische Methoden an, die von Goldman und Xia entwickelt wurden, um zu beweisen, dass die Wirkung ergodisch ist. ix Perceval: Dans la vie, j'avais deux ennemis: le vocabulaire et les épinards. Maintenant, j'ai la botte secrète et je bouffe plus d'épinards. Merci, de rien, au revoir messieurs-dames. Kaamelott Livre II, La Botte secrète II J'invite mon lecteur à imaginer, à cet endroit, une tirade inspirée comme celle d'Otis, interprété par l'excellent Édouard Baer. Évidemment que la route du doctorat était sinueuse. Je suis heureux que les contours aient été adoucis par toutes les formidables personnes qui m'ont accompagné durant ces quatre dernières années. Il a fallu du courage pour trouver de la motivation dans l'ingratitude de la recherche mathématique. L'écriture d'une thèse dans un domaine aussi abstrait des sciences fondamentales est une tâche sisyphéenne. Le boulet finit néanmoins, en de rares occasions, par tenir en équilibre au sommet de la montagne, du moins brièvement, offrant une bouffée de satisfaction méritée à celui qui le pousse. La joie du succès est personnelle. Ce serait mentir que de dire que je l'ai fait pour autrui. Celui qui recherche les lauriers ferait mieux d'aller jouer à la pétanque. Je dédicace cette thèse à Alain qui a été un magnifique compagnon de route depuis un quart de siècle. Au-delà de notre complicité (surtout dans la déconnade), je te suis redevable d'avoir été cette source d'inspiration mathématique. Si je vole aujourd'hui, confiant, de mes propres ailes, c'est en grande partie parce que j'avais le meilleur des lièvres au départ de la course. xi My gratitude goes, first and foremost, to my advisors Peter and Anna W. for guiding me since the beginning. I enjoyed discussing math with you and always found it very inspiring. Vielen Dank! A big thank goes to Andy for your wild enthusiasm and your generosity. It was a pleasure to have you as a mentor. I am grateful to all the people I could always annoy with my questions, especially Bea whose office door was always open. I am indebted to all my colleagues in Heidelberg. Grazie Marta e Valerio! Merci à vous deux pour votre infinie générosité et pour votre bonne humeur. C'est un vrai plaisir de partager une amitié avec vous. Danke auch an Max S. I envy your calm sometimes (and also your strength when it comes to bouldering). Grazie Simone; you made it easier to survive Heidelberg when the city showed its dull side. Un grand merci à Brice pour avoir pris le temps de répondre à toutes mes questions et pour toutes les soirées passées à blitzer. Bon vent à toi! My gratitude goes to Fernando, Max R., Thi, Colin, Gabriele V. and James for enlightening discussions related to this work. Vielen Dank Irene und Anna-Maria, my pre-exile office mates, for the unexpected birthday wishes, and for hearing my doubts and sharing yours. I wish you all the best! The last four years would have been very boring without the time I spent with colleagues at the bouldering gym. Thanks to Mari for your constant sunny disposition, to my pull-ups partner Kevin, and to Alexandre, Johannes, Florian and Max S. Finally, I would like to thank my colleagues Urs,Arnaud Maretwork_mx2hvhlo25ftbbnlmcutlxd6eyVlatakisGkaragkounis_columbia_0054D_17419.pdf
https://scholar.archive.org/work/b7t2wwdek5durbpmlwlw76zexe
Dimitris I wouldn't have been able to sort out my feelings among university choices. For all that, I thank you dearly my good friend. Furthermore, a special thanks should be expressed to Father Panayotis, the community of Saint Gerasimos and Ioannis-Angelos Lagan's whose friendship during the Covid-19 pandemic was my only escape from this disease tragedy. At a more academic tone again, there are three Greek Professors that played a significant role in this journey, Georgios Piliouras, Panayotis Mertikopoulos and Ioannis Panageas. George, thanks for your continuous help and teaching me the self-confidence in an era and area of ML. Panayotis, thanks for never being bothered by my interminable list of questions and lending me to use your incredible Oxford style English phrases. Ioanni, thanks for teaching us that audacity sometimes serves science just as well as humility. A convex combination of yours consist the fondest researcher I have ever met; Without you, I certainly would have been a different scientist. I hope that the terminal station of the trip will "reimburse" all of us. Closing this section, I cannot avoid looking back confessing that the decision to leave Greece was, without a doubt, the hardest one that I have made in my entire life. Of course, this is hardly xv the place to get into the reasons behind this decision, except to mention that one of the most important ones had to do with the friends that I had made in Greece and who had remained an ocean and several time zones away. Thus, I can not forget to thank all my friends and professors from the lab where I completed my undergraduate degree in Greece: Thanasis, Natalia, Giorgos and Ilias, Manolis and Kostas, Fotis and Vasilis, Eleni and Chara, Makis and Kyriakos, Dimitris, Aris, Panaro, Nikolas, Stathis, I am grateful to all of you for never giving up in communicating with me and supporting me throughout the years of my PhD, despite the long distance. I might never have decided to embark upon a life of computer science research if I have not met you. Before addressing my ultimate thanks to my blood family, there is a larger and deeper family that have brought always smile to my face (even when there is nothing to smile about), along with your big always accepting hug.:unavwork_b7t2wwdek5durbpmlwlw76zexeAsymptotic mapping class groups of Cantor manifolds and their finiteness properties
https://scholar.archive.org/work/i5ss25hbhfhl5mj2ix3rpqr3oe
A Cantor manifold 𝒞 is a non-compact manifold obtained by gluing (holed) copies of a fixed compact manifold Y in a tree-like manner. Generalizing classical families of groups due to Brin, Dehornoy, and Funar- Kapoudjian, we introduce the asymptotic mapping class group ℬ of 𝒞, whose elements are proper isotopy classes of self-diffeomorphisms of 𝒞 that are eventually trivial. The group ℬ happens to be an extension of a Higman-Thompson group by a direct limit of mapping class groups of compact submanifolds of 𝒞. We construct an infinite-dimensional contractible cube complex 𝔛 on which ℬ acts. For certain well-studied families of manifolds, we prove that ℬ is of type F_∞ and that 𝔛 is CAT(0); more concretely, our methods apply for example when Y is diffeomorphic to 𝕊^1 ×𝕊^1, 𝕊^2×𝕊^1, or 𝕊^n ×𝕊^n for n≥ 3. In these cases, ℬ contains, respectively, the mapping class group of every compact surface with boundary; the automorphism group of the free group on k generators for all k; and an infinite family of (arithmetic) symplectic or orthogonal groups. In particular, if Y ≅𝕊^2 or 𝕊^1 ×𝕊^1, our result gives a positive answer to a question of Funar–Kapoudjian–Sergiescu. In addition, for Y≅𝕊^1 ×𝕊^1 or 𝕊^2×𝕊^1, the homology of ℬ coincides with the stable homology of the relevant mapping class groups, as studied by Harer and Hatcher–Wahl.Javier Aramayona, Kai-Uwe Bux, Jonas Flechsig, Nansen Petrosyan, Xiaolei Wuwork_i5ss25hbhfhl5mj2ix3rpqr3oeThu, 23 Dec 2021 00:00:00 GMTTopological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type
https://scholar.archive.org/work/jvbxmsqinvfclca4ufcbvtjoey
We study the n-point differentials corresponding to Kadomtsev-Petviashvili tau functions of hypergeometric type (also known as Orlov-Scherbin partition functions), with an emphasis on their ħ^2-deformations and expansions. Under the naturally required analytic assumptions, we prove certain higher loop equations that, in particular, contain the standard linear and quadratic loop equations, and thus imply the blobbed topological recursion. We also distinguish two large families of the Orlov-Scherbin partition functions that do satisfy the natural analytic assumptions, and for these families we prove in addition the so-called projection property and thus the full statement of the Chekhov-Eynard-Orantin topological recursion. A particular feature of our argument is that it clarifies completely the role of ħ^2-deformations of the Orlov-Scherbin parameters for the partition functions, whose necessity was known from a variety of earlier obtained results in this direction but never properly understood in the context of topological recursion. As special cases of the results of this paper one recovers new and uniform proofs of the topological recursion to all previously studied cases of enumerative problems related to weighted double Hurwitz numbers. By virtue of topological recursion and the Grothendieck-Riemann-Roch formula this, in turn, gives new and uniform proofs of almost all ELSV-type formulas discussed in the literature.Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian, Sergey Shadrinwork_jvbxmsqinvfclca4ufcbvtjoeyThu, 23 Dec 2021 00:00:00 GMT