BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Stephanie van Willigenburg (University of British Columbia) DTSTART:20210618T150000Z DTEND:20210618T160000Z DTSTAMP:20260422T212609Z UID:ACPMS/1 DESCRIPTION:Title: Th e e-positivity of chromatic symmetric functions\nby Stephanie van Will igenburg (University of British Columbia) as part of Algebraic and Combina torial Perspectives in the Mathematical Sciences\n\n\nAbstract\nThe chroma tic polynomial was generalized to the chromatic symmetric function by Stan ley in his seminal 1995 paper. This function is currently experiencing a f lourishing renaissance\, in particular the study of the positivity of chro matic symmetric functions when expanded into the basis of elementary symme tric functions\, that is\, e-positivity.\nIn this talk we approach the que stion of e-positivity from various angles. Most pertinently we resolve the 1995 statement of Stanley that no known graph exists that is not contract ible to the claw\, and whose chromatic symmetric function is not e-positiv e.\n\nThis is joint work with Soojin Cho\, Samantha Dahlberg\, Angele Fole y and Adrian She\, and no prior knowledge is assumed.\n\nPlease note that this talk starts at 17:00 (GMT+2) instead of the usual time.\n LOCATION:https://researchseminars.org/talk/ACPMS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Amy Pang (Hong Kong Baptist University) DTSTART:20210625T130000Z DTEND:20210625T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/2 DESCRIPTION:Title: Ma rkov chains from linear operators and Hopf algebras\nby Amy Pang (Hong Kong Baptist University) as part of Algebraic and Combinatorial Perspecti ves in the Mathematical Sciences\n\n\nAbstract\nIf you study a linear oper ator that expands positively in some basis\, then your results may be appl icable to a Markov chain\, whose transition probabilities are given by the matrix of the operator. This is the idea behind the theory of random walk s on groups and monoids\, where the eigen-data of the operator informs the long-term behaviour of the chain. We point out a lesser-known advantage o f this framework: if the linear operator descends to a specific subquotien t of its domain\, then the corresponding Markov chain admits a projection / lumping. We apply this to a coproduct-then-product operator on Hopf alge bras\, to explain Jason Fulman's observation regarding the RSK-shape under card-shuffling. I hope this talk will enable and inspire you to explore n ew examples.\n LOCATION:https://researchseminars.org/talk/ACPMS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Maciej Dołęga (Polish Academy of Sciences) DTSTART:20210702T130000Z DTEND:20210702T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/3 DESCRIPTION:by Maciej Dołęga (Polish Academy of Sciences) as part of Alg ebraic and Combinatorial Perspectives in the Mathematical Sciences\n\nAbst ract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Carolina Benedetti (Universidad de los Andes\, Bogotá) DTSTART:20210709T130000Z DTEND:20210709T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/4 DESCRIPTION:by Carolina Benedetti (Universidad de los Andes\, Bogotá) as part of Algebraic and Combinatorial Perspectives in the Mathematical Scien ces\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Susama Agarwala (University of Hamburg) DTSTART:20210903T130000Z DTEND:20210903T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/5 DESCRIPTION:by Susama Agarwala (University of Hamburg) as part of Algebrai c and Combinatorial Perspectives in the Mathematical Sciences\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Frédéric Chapoton (CNRS\, Strasbourg) DTSTART:20210910T130000Z DTEND:20210910T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/6 DESCRIPTION:Title: Mu ltiple zeta values and zinbiel algebras\nby Frédéric Chapoton (CNRS\ , Strasbourg) as part of Algebraic and Combinatorial Perspectives in the M athematical Sciences\n\n\nAbstract\nWe will explain the construction\, usi ng the notion of Zinbiel algebra\, of some commutative subalgebras $C_{u\, v}$ inside an algebra of formal iterated integrals. There is a quotient ma p from this algebra of formal iterated integrals to the algebra of motivic multiple zeta values. Restricting this quotient map to the subalgebras $C _{u\,v}$ gives a morphism of graded commutative algebras with the same gen erating series. This is conjectured to be generically an isomorphism. When $u+v = 0$\, the image is instead a sub-algebra of the algebra of motivic multiple zeta values.\n LOCATION:https://researchseminars.org/talk/ACPMS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Chaitanya Leena Subramaniam (Université Paris Diderot) DTSTART:20210917T130000Z DTEND:20210917T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/7 DESCRIPTION:Title: De pendent type theory and higher algebraic structures\nby Chaitanya Leen a Subramaniam (Université Paris Diderot) as part of Algebraic and Combina torial Perspectives in the Mathematical Sciences\n\n\nAbstract\nIn classic al universal algebra\, every family of algebraic structures (such as monoi ds\, groups\, rings\, modules\, small categories\, operads\, sheaves) can be classified by a syntactic (algebraic or essentially algebraic) equation al theory. A cornerstone of universal algebra is the equivalence between a lgebraic theories and finitary monads on the category of sets\, due to Law vere\, B\\'enabou and Linton. Higher algebraic structures (such as loop sp aces\, E-k spaces\, infinity-categories\, infinity-operads and their modul es and algebras\, stacks\, spectra) are algebraic structures up to homotop y in spaces ("spaces" = topological spaces\, simplicial sets or any other model of homotopy types). It is a long-standing presupposition among homot opy type theorists that the dependent types introduced by Martin-L\\"of ar e particularly well-suited to providing syntactic theories and a universal algebra for higher algebraic structures. In this talk\, we will see a (fe w) definition(s) of "dependently sorted/typed algebraic theory" and descri be a monad-theory equivalence strictly generalising that of Lawvere-Bénab ou-Linton. With respect to their Set-valued models\, dependently sorted al gebraic theories have the same expressive power as essentially algebraic t heories. However\, as we will see in this talk\, dependently sorted algebr aic theories have the advantage of having a good theory of models up-to-ho motopy in spaces\, which generalises the theory of homotopy-models of alge braic theories due to Schwede\, Badzioch\, Rezk and Bergner. We will see t hat many familiar algebraic structures (such as n-categories\, omega-categ ories\, coloured planar operads\, opetopic sets) are very naturally seen t o be models of dependently sorted algebraic theories. The crux of these re sults is a correspondence between the dependent sorts/types of any depende ntly sorted algebraic theory T\, and a certain "cellularity" underlying ev ery algebraic structure described by T (i.e. every T-model). The goal of t his talk will be to explain this correspondence between type dependency an d cellularity\, and why this cellularity marries well with homotopy theory .\n LOCATION:https://researchseminars.org/talk/ACPMS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Gunnar Fløystad (University of Bergen) DTSTART:20210924T130000Z DTEND:20210924T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/8 DESCRIPTION:Title: Sh ift modules\, strongly stable ideals\, and their dualities\nby Gunnar Fløystad (University of Bergen) as part of Algebraic and Combinatorial Pe rspectives in the Mathematical Sciences\n\n\nAbstract\nPolynomial rings ov er a field $k$ are the prime objects in algebra. Ideals in polynomial ring s are the prime objects relating algebra and geometry via the zero set of the ideal.\n\nTo understand ideals in a polynomial ring\, a common approac h is to see what simpler ideals they degenerate to\, for instance what mon omial ideals. But what are the most degenerate ideals you can find? Those that cannot be degenerated any further? These are the so-called Borel-fixe d ideals\, or\, when the field k has characteristic zero\, the strongly st able ideals. This class is for instance the essential tool for understandi ng numerical invariants of ideals in polynomial rings.\n\nWe enrich the se tting of strongly stable ideals by:\n\n1. Extending them to a category of modules\n\n2. Investigating the recently discovered duality on these ideal s\n\n3. Getting a new type of projective resolution of such ideals\n\n4. L etting the ambient polynomial ring be infinite dimensional\n LOCATION:https://researchseminars.org/talk/ACPMS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Franz Herzog (The University of Edinburgh) DTSTART:20211001T130000Z DTEND:20211001T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/9 DESCRIPTION:Title: Th e Hopf algebra of IR divergences of Feynman graphs\nby Franz Herzog (T he University of Edinburgh) as part of Algebraic and Combinatorial Perspec tives in the Mathematical Sciences\n\n\nAbstract\nIt is by now very well k nown that the structure of UV divergences Feynman Integrals\, and their as sociated graphs\, can be described elegantly in a Hopf algebra originally developed by Kreimer and Connes. Beyond UV divergences Feynman Integrals a lso suffer from IR\, long-distance\, divergences. I will present a new Hop f-algebraic formulation which allows to simultaneously treat both the IR a nd the UV. Remarkably in this framework the IR and UV counterterm maps are inverse to each other on the group of characters of the Hopf algebra.\n LOCATION:https://researchseminars.org/talk/ACPMS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Sophie Spirkl (University of Waterloo) DTSTART:20211022T130000Z DTEND:20211022T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/10 DESCRIPTION:Title: M odular relations for the Tutte symmetric function\nby Sophie Spirkl (U niversity of Waterloo) as part of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nThe Tutte symmetric function XB generalizes both the Tutte polynomial and the chromatic symmetric funct ion X. In this talk\, I'll discuss a modular relation for XB analogous to the Orellana-Scott relation for X\, general results for modular relations for XB and X\, and applications.\nJoint work with Logan Crew.\n LOCATION:https://researchseminars.org/talk/ACPMS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Gerald Dunne (University of Connecticut) DTSTART:20211029T130000Z DTEND:20211029T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/11 DESCRIPTION:Title: R esurgent Trans-series in Hopf-Algebraic Dyson-Schwinger Equations\nby Gerald Dunne (University of Connecticut) as part of Algebraic and Combinat orial Perspectives in the Mathematical Sciences\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Bérénice Delcroix-Oger (Université de Paris) DTSTART:20211217T140000Z DTEND:20211217T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/12 DESCRIPTION:by Bérénice Delcroix-Oger (Université de Paris) as part of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\nA bstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Gilliers (University of Toulouse) DTSTART:20211008T130000Z DTEND:20211008T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/13 DESCRIPTION:Title: B inary trees\, operads and Dykema’s T-transform in Free Probability\n by Nicolas Gilliers (University of Toulouse) as part of Algebraic and Comb inatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nIn this talk\, we shall discuss an operadic perspective on K. Dykema’s twisted factorization formula for the operator-valued T-transform in free probabil ity. To begin with\, we introduce in the general setting of an operad with multiplication two group products on formal series of operators\, besides the one introduced by F. Chapoton. We explain how those products relate b y means of certain transformation\, that we call (abstract) T-transform\, borrowing terminology from free probability. Specializing in the endomorph ism operad gives a new perspective on the twisted factorization of the T-t ransform and to multiplicative free convolution. We will discuss connectio ns to the work of A. Frabetti and C. Brouder by specializing our construct ion to the duoidal and dendriform operads.\n LOCATION:https://researchseminars.org/talk/ACPMS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Yannic Vargas (University of Potsdam) DTSTART:20211015T130000Z DTEND:20211015T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/14 DESCRIPTION:Title: M onomial bases for combinatorial Hopf algebras\nby Yannic Vargas (Unive rsity of Potsdam) as part of Algebraic and Combinatorial Perspectives in t he Mathematical Sciences\n\n\nAbstract\nThe algebraic structure of a Hopf algebra can often be understood in terms of a poset on the underlying fami ly of combinatorial objects indexing a basis. For example\, the Hopf algeb ra of quasisymmetric functions is generated (as a vector space) by composi tions and admits a fundamental (F) basis and a monomial (M) basis\, relate d by the refinement poset on compositions. Analogous bases can be consider ed for other Hopf algebras\, with similar properties to the F basis\, e.g. a product described by some notion of shuffle\, and a coproduct following some notion of deconcatenation. We give axioms for how these generalised shuffles and deconcatentations should interact with the underlying poset s o that a monomial-like basis can be analogously constructed\, generalising the approach of Aguiar and Sottile. We also find explicit positive formul as for the multiplication on monomial basis and a cancellation-free and gr ouping-free formula for the antipode of monomial elements. We apply these results on classical and new Hopf algebras\, related by tree-like structur es.\nThis is based on "Hopf algebras of parking functions and decorated pl anar trees"\, a joint work with Nantel Bergeron\, Rafael Gonzalez D'Leon\, Amy Pang and Shu Xiao Li.\n LOCATION:https://researchseminars.org/talk/ACPMS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonard Schmitz (University of Greifswald) DTSTART:20230120T140000Z DTEND:20230120T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/15 DESCRIPTION:Title: T wo-parameter sums signatures and corresponding quasisymmetric functions\nby Leonard Schmitz (University of Greifswald) as part of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Jaiung Jun (SUNY at New Paltz) DTSTART:20230317T140000Z DTEND:20230317T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/16 DESCRIPTION:Title: O n the Hopf algebra of multi-complexes\nby Jaiung Jun (SUNY at New Palt z) as part of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nHopf algebras appear naturally in combinatorics i n the following way: For a given class of combinatorial objects (such as g raphs or matroids)\, basic operations (such as assembly and disassembly op erations) often can be encoded in the algebraic structure of a Hopf algebr a. One then hopes to use algebraic identities of a Hopf algebra to return to combinatorial identities of combinatorial objects of interest. In this talk\, I will introduce a general class of combinatorial objects\, which w e call multi-complexes. They simultaneously generalize graphs\, hypergraph s and simplicial and delta complexes. I will describe the structure of the Hopf algebra of multi-complexes by finding an explicit basis of the space of primitives. This is joint work with Miodrag Iovanov.\n LOCATION:https://researchseminars.org/talk/ACPMS/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Annika Burmester (Bielefeld University) DTSTART:20230331T130000Z DTEND:20230331T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/17 DESCRIPTION:Title: P ost-Lie algebras related to multiple (q-)zeta values\nby Annika Burmes ter (Bielefeld University) as part of Algebraic and Combinatorial Perspect ives in the Mathematical Sciences\n\n\nAbstract\nMultiple zeta values beca me of more interest over the last 25 years due to their appearance in vari ous fields of mathematics and also physics. First\, we will describe their algebraic structure in terms of Hoffman’s quasi-shuffle algebras\, whic h are certain deformations of the usual shuffle product. Following Racinet this allows to relate a post-Lie algebra to the multiple zeta values\, th e double shuffle Lie algebra equipped with the Ihara bracket\, which gives a new insight into the algebraic structure of multiple zeta values. We ar e interested in an analog approach for multiple q-zeta values\, which are certain q-series degenerating to multiple zeta values for the limit q to 1 . In particular\, we will explain some results towards a post-Lie algebra related to multiple q-zeta values.\n LOCATION:https://researchseminars.org/talk/ACPMS/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Karine Beauchard (ENS Rennes) DTSTART:20230414T130000Z DTEND:20230414T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/18 DESCRIPTION:Title: O n expansions for nonlinear systems\, error estimates and convergence issue s\nby Karine Beauchard (ENS Rennes) as part of Algebraic and Combinato rial Perspectives in the Mathematical Sciences\n\n\nAbstract\nExplicit for mulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular\, intrinsic formulas allowing to decouple time-dependent features from geometry-dependent features of t he solution have been extensively studied.\nFirst\, we give a didactic rev iew of classical expansions for formal linear differential equations\, inc luding the celebrated Magnus expansion (associated with coordinates of the first kind) and Sussmann’s infinite product expansion (associated with coordinates of the second kind). Inspired by quantum mechanics\, we introd uce a new mixed expansion\, designed to isolate the role of a time-invaria nt drift from the role of a time-varying perturbation.\nSecond\, in the co ntext of nonlinear ordinary differential equations driven by regular vecto r fields\, we give rigorous proofs of error estimates between the exact so lution and finite approximations of the formal expansions. In particular\, we derive new estimates focusing on the role of time-varying perturbation s.\nThird\, we investigate the local convergence of these expansions. In p articular\, we exhibit arbitrarily small analytic vector fields for which the convergence of the Magnus expansion fails\, even in very weak senses.\ nEventually\, we derive approximate direct intrinsic representations for t he state\, particularly well designed for applications in control theory.\ n LOCATION:https://researchseminars.org/talk/ACPMS/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Darij Grinberg DTSTART:20230428T130000Z DTEND:20230428T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/19 DESCRIPTION:by Darij Grinberg as part of Algebraic and Combinatorial Persp ectives in the Mathematical Sciences\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Gunnar Fløystad DTSTART:20230512T130000Z DTEND:20230512T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/20 DESCRIPTION:by Gunnar Fløystad as part of Algebraic and Combinatorial Per spectives in the Mathematical Sciences\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Chiara Meroni DTSTART:20230526T130000Z DTEND:20230526T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/21 DESCRIPTION:Title: P ath signatures in convex geometry\nby Chiara Meroni as part of Algebra ic and Combinatorial Perspectives in the Mathematical Sciences\n\n\nAbstra ct\nHow can one compute the volume of the convex hull of a curve? I will t ry to answer this question\, for special families of curves. This is a joi nt work with Carlos Améndola and Darrick Lee. We generalise the class of curves for which a certain integral formula works\, using the technique of signatures. I will then give a geometric interpretation of this volume fo rmula in terms of lengths and areas\, and conclude with examples and an op en conjecture.\n LOCATION:https://researchseminars.org/talk/ACPMS/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Emilie Purvine DTSTART:20230609T140000Z DTEND:20230609T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/22 DESCRIPTION:Title: A pplied Topology for Discrete Structures\nby Emilie Purvine as part of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\ nAbstract\nDiscrete structures have a long history of use in applied mathe matics. Graphs and hypergraphs provide models of social networks\, biologi cal systems\, academic collaborations\, and much more. Network science\, a nd more recently hypernetwork science\, have been used to great effect in analyzing these types of discrete structures. Separately\, the field of ap plied topology has gathered many successes through the development of pers istent homology\, mapper\, sheaves\, and other concepts. Recent work by ou r group has focused on the convergence of these two areas\, developing and applying topological concepts to study discrete structures that model rea l data. This talk will survey our body of work in this area showing our wo rk in both the theoretical and applied spaces. Theory topics will include an introduction to hypernetwork science and its relation to traditional ne twork science\, topological interpretations of graphs and hypergraphs\, an d dynamics of topology and network structures. I will show examples of how we are applying each of these concepts to real data sets.\n LOCATION:https://researchseminars.org/talk/ACPMS/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Emanuele Verri (Universität Greifswald) DTSTART:20230623T130000Z DTEND:20230623T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/23 DESCRIPTION:Title: C onjoined permutation patterns\nby Emanuele Verri (Universität Greifsw ald) as part of Algebraic and Combinatorial Perspectives in the Mathematic al Sciences\n\n\nAbstract\nSome time ago\, Bandt introduced the concept of "permutation entropy" which proved very effective in the analysis of time series.\nThis index is based on certain permutation patterns.\nPermutatio n patterns play indeed a very central role in many areas of discrete mathe matics.\nMore recently\, in algebraic combinatorics\, Vargas introduced th e superinfiltration Hopf algebra whose operations behave well with respect to occurrences of permutation patterns.\nInspired by both these works\, w e introduce a new Hopf algebra which also includes the patterns used by Ba ndt.\nIts algebraic operations behave well with respect to occurrences of permutation patterns where is also specified whether values are consecutiv e or arbitrarily far apart.\nTo encode whether two values are consecutive\ , we use interval partitions of finite subsets of positive integers and al so introduce a new Hopf algebra on interval partitions.\nThis is joint wor k with Joscha Diehl.\n LOCATION:https://researchseminars.org/talk/ACPMS/23/ END:VEVENT BEGIN:VEVENT SUMMARY:TBA DTSTART:20230707T130000Z DTEND:20230707T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/24 DESCRIPTION:by TBA as part of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Olson-Harris (University of Waterloo) DTSTART:20230918T130000Z DTEND:20230918T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/25 DESCRIPTION:by Nick Olson-Harris (University of Waterloo) as part of Algeb raic and Combinatorial Perspectives in the Mathematical Sciences\n\nAbstra ct: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Kasia Rejzner (University of York) DTSTART:20230929T130000Z DTEND:20230929T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/26 DESCRIPTION:Title: P erturbative algebraic quantum field theory (introduction and examples) \nby Kasia Rejzner (University of York) as part of Algebraic and Combinato rial Perspectives in the Mathematical Sciences\n\n\nAbstract\nIn this talk I will introduce the framework perturbative algebraic quantum field theor y. It allows one to combine the method of Epstein-Glaser renormalisation w ith the idea of BV quantization\, commonly applied to quantization of gaug e theories. It straightforwardly generalizes to theories on a large class of Lorentzian manifolds. The same formalism can also be applied when one r eplaces the manifold with a finite collection of points\, equipped with a partial order relation (modelling the causal order).\n LOCATION:https://researchseminars.org/talk/ACPMS/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Olson-Harris DTSTART:20231013T130000Z DTEND:20231013T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/27 DESCRIPTION:by Nick Olson-Harris as part of Algebraic and Combinatorial Pe rspectives in the Mathematical Sciences\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Alejandro Cabrera (Universidade Federal do Rio de Janeiro) DTSTART:20231027T130000Z DTEND:20231027T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/28 DESCRIPTION:Title: A bout local symplectic groupoids and applications\nby Alejandro Cabrera (Universidade Federal do Rio de Janeiro) as part of Algebraic and Combina torial Perspectives in the Mathematical Sciences\n\n\nAbstract\nIn this ta lk\, we will review the notion of local symplectic groupoid and its relati on to Poisson geometry. We then summarize some recent results involving ex plicit constructions and their relation to quantization. Finally\, we will comment on applications to discretization of hamiltonian flows on Poisson manifolds.\n LOCATION:https://researchseminars.org/talk/ACPMS/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Vallette DTSTART:20231117T140000Z DTEND:20231117T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/30 DESCRIPTION:by Bruno Vallette as part of Algebraic and Combinatorial Persp ectives in the Mathematical Sciences\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Matilde Marcolli DTSTART:20231201T140000Z DTEND:20231201T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/31 DESCRIPTION:by Matilde Marcolli as part of Algebraic and Combinatorial Per spectives in the Mathematical Sciences\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Oliver Pechenik (University of Waterloo) DTSTART:20231215T140000Z DTEND:20231215T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/32 DESCRIPTION:Title: Q uasisymmetric Schubert calculus\nby Oliver Pechenik (University of Wat erloo) as part of Algebraic and Combinatorial Perspectives in the Mathemat ical Sciences\n\n\nAbstract\nWe introduce projective schemes that are anal ogues of the James reduced product construction from homotopy theory and b egin to develop a Schubert calculus for such spaces. This machinery yields K-theoretic and T-equivariant analogues of classic quasisymmetric functio n theory. Based on joint works with Matt Satriano.\n LOCATION:https://researchseminars.org/talk/ACPMS/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Dan Shiebler (Abnormal Security) DTSTART:20240126T140000Z DTEND:20240126T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/33 DESCRIPTION:Title: L earning with Kan Extensions\nby Dan Shiebler (Abnormal Security) as pa rt of Algebraic and Combinatorial Perspectives in the Mathematical Science s\n\n\nAbstract\nA common problem in machine learning is "use this functio n defined over this small set to generate predictions over that larger set ." Extrapolation\, interpolation\, statistical inference and forecasting a ll reduce to this problem. The Kan extension is a powerful tool in categor y theory that generalizes this notion. In this work we explore application s of the Kan extension to machine learning problems. We begin by deriving a simple classification algorithm as a Kan extension and experimenting wit h this algorithm on real data. Next\, we use the Kan extension to derive a procedure for learning clustering algorithms from labels and explore the performance of this procedure on real data.\n LOCATION:https://researchseminars.org/talk/ACPMS/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Nikolas Tapia (Weierstrass Institute) DTSTART:20240209T140000Z DTEND:20240209T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/34 DESCRIPTION:Title: B ranched Itô Formula and natural Itô-Stratonovich isomorphism\nby Nik olas Tapia (Weierstrass Institute) as part of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nBranched rough pa ths define integration theories that may fail to satisfy the integration b y parts identity. The projection of the Connes-Kreimer Hopf algebra (\\(\\ mathcal{H}_{\\mathrm{CK}}\\)) onto its primitive elements defined by Broad hurst-Kreimer and Foissy\, allows us to view \\(\\mathcal{H}_{\\mathrm{CK} }\\) as a commutative \\(\\mathbf{B}_\\infty\\)-algebra and thus to write an explicit change-of-variable formula for solutions to rough differential equations (RDEs)\, which restricts to the well-known Itô formula for sem imartingales. When compared with Kelly’s approach using bracket extensio ns\, this formula has the advantage of only depending on internal structur e. We proceed to define an isomorphism between \\(\\mathcal{H}_{\\mathrm{C K}}\\) and \\(\\operatorname{Sh}(\\mathcal{P})\\) (the shuffle algebra ove r primitives)\, which we compare with the previous constructions of Hairer -Kelly and Boedihardjo-Chevyrev: while all three allow one to write branch ed RDEs as RDEs driven by geometric rough paths taking values in a larger space\, the key feature of our isomorphism is that it is natural when \\(\ \mathcal{H}_{\\mathrm{CK}}\\) and \\(\\operatorname{Sh}(\\mathcal{P})\\) a re viewed as covariant functors \\(\\mathsf{Vec}\\to\\mathsf{Hopf}\\). Our natural isomorphism extends Hoffman’s exponential for the quasi shuffle algebra\, and in particular the usual Itô-Stratonovich correction formul a for semimartingales. Special emphasis is placed on the 1-dimensional cas e\, in which certain rough path terms can be expressed as polynomials in t he trace path indexed by \\(\\mathcal{P}\\)\, which for semimartingales re strict to the well-known Kailath-Segall polynomials.\n\nThis talk is based on joint work with E. Ferrucci and C. Bellingeri.\n LOCATION:https://researchseminars.org/talk/ACPMS/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Hannes Kern (TU Berlin) DTSTART:20240301T140000Z DTEND:20240301T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/35 DESCRIPTION:Title: R ough Flow techniques on manifolds\nby Hannes Kern (TU Berlin) as part of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n \n\nAbstract\nIn 2020\, Armstrong et al managed to explicitly write down D avie’s formula of the solution of a non-geometric RDE on a manifold for the level N = 2. In this talk\, we introduce a new notion\, called pseudo bialgebra map\, which allows us to construct similar expansions for higher level rough pahs living in general Hopf algebras. To do this\, we prove a local version of Bailleul’s sewing lemma for flows. Finally\, we go ove r previous results and show that they do give rise to pseudo bialgebra map s. Based on joint work with Terry Lyons.\n LOCATION:https://researchseminars.org/talk/ACPMS/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Ruggero Bandiera (Sapienza Università di Roma) DTSTART:20240315T140000Z DTEND:20240315T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/36 DESCRIPTION:Title: C umulants\, Koszul brackets and homological perturbation theory for commuta tive BVoo and IBLoo algebras\nby Ruggero Bandiera (Sapienza Universit à di Roma) as part of Algebraic and Combinatorial Perspectives in the Mat hematical Sciences\n\n\nAbstract\nn the first part of this talk we shall r eview the classical homotopy transfer theorem in the context of Aoo and Lo o algebras. We shall explain how the usual proof of this result for Aoo al gebras\, based on the tensor trick and the homological perturbation lemma\ , can be adapted to Loo algebras using a symmetrized version of the tensor trick. In the course of the discussion we shall review the construction o f cumulants and Koszul brackets (as well as their coalgebraic analogs): th ese are graded symmetric multilinear maps associated respectively to a mor phism of graded commutative algebras $f\\colon A \\to B$ or to an endomorp hism $d\\colon A \n\\to A$\, measuring the deviation of f from being an al gebra morphism in the first case\, and the deviation of d from being an al gebra derivation in the second case. A key technical lemma will be that un der certain assumptions on the involved contraction\, these are compatible with homotopy transfer in an appropriate sense. In the second part of the talk we shall review commutative BVoo algebra in the sense of Kravchenko: as an application of our previous discussion we shall introduce a new def inition of morphisms between these objects in terms of cumulants. Moreover \, we shall explain how to use homological perturbation theory to get a ho motopy transfer theorem for commutative BVoo algebras\, under certain assu mptions on the involved contraction. Finally\, IBLoo algebras\, that is\, commutative BVoo algebras whose underlying algebra is free\, are known to be a model for involutive Lie bialgebras up to coherent homotopies\, and h ave recently found several applications in string topology and symplectic field theory. \nAs an application of our results\, we shall explain how to obtain a homotopy transfer theorem for IBLoo algebras via the symmetrized tensor trick and the homological perturbation lemma.\n LOCATION:https://researchseminars.org/talk/ACPMS/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Joswig (TU Berlin) DTSTART:20240223T140000Z DTEND:20240223T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/37 DESCRIPTION:Title: Q uantum automorphisms of matroids\nby Michael Joswig (TU Berlin) as par t of Algebraic and Combinatorial Perspectives in the Mathematical Sciences \n\n\nAbstract\nMotivated by the vast literature of quantum automorphism g roups of graphs\, we define and study quantum automorphism groups of matro ids. A key feature of quantum groups is that there are many quantizations of a classical group\, and this phenomenon manifests in the cryptomorphic characterizations of matroids. Our primary goals are to understand\, using theoretical and computational techniques\, the relationship between these quantum groups and to find when these quantum groups exhibit quantum symm etry. Finally\, we prove a matroidal analog of Lovász's theorem character izing graph isomorphisms in terms of homomorphism counts.\n\nJoint work wi th Daniel Corey\, Julien Schanz\, Marcel Wack\, and Moritz Weber.\n LOCATION:https://researchseminars.org/talk/ACPMS/37/ END:VEVENT BEGIN:VEVENT SUMMARY:William Turner (Imperial College London) DTSTART:20240405T130000Z DTEND:20240405T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/38 DESCRIPTION:Title: F ree probability\, path developments and signature kernels as universal sca ling limits\nby William Turner (Imperial College London) as part of Al gebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\nA bstract\nScaling limits of random developments of a path into a matrix Lie Group have recently been used to construct signature-based kernels on pat h space\, while mitigating some of the dimensionality challenges that come with using signatures directly. Muça Cirone et al. have established a co nnection between the scaling limit of general linear group developments wi th Gaussian vector fields and the ordinary signature kernel\, while Lou et al. utilised unitary group developments and previous work of Chevyrev and Lyons to construct a path characteristic function distance. By leveraging the tools of random matrix theory and free probability theory\, we are ab le to provide a unified treatment of the limits in both settings under gen eral assumptions on the vector fields. For unitary developments\, we show that the limiting kernel is given by the contraction of a signature agains t the monomials of freely independent semicircular random variables. Using the Schwinger-Dyson equations\, we show that this kernel can be obtained by solving a novel quadratic functional equation.\n LOCATION:https://researchseminars.org/talk/ACPMS/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Helena Bergold (Freie Universität Berlin) DTSTART:20240419T130000Z DTEND:20240419T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/39 DESCRIPTION:Title: A n Extension Theorem for Signotopes\nby Helena Bergold (Freie Universit ät Berlin) as part of Algebraic and Combinatorial Perspectives in the Mat hematical Sciences\n\n\nAbstract\nIn 1926\, Levi showed that\, for every p seudoline arrangement $A$ and two\npoints in the plane\, $A$ can be extend ed by a pseudoline which contains\nthe two prescribed points. Later extend ability was studied for\narrangements of pseudohyperplanes in higher dimen sions. While the\nextendability of an arrangement of proper hyperplanes in R^d with a\nhyperplane containing $d$ prescribed points is trivial\, Rich ter-Gebert\nfound an arrangement of pseudoplanes in R^3 which cannot be ex tended\nwith a pseudoplane containing two particular prescribed points.\nI n this talk\, we investigate the extendability of signotopes\, which are\n a combinatorial structure encoding a rich subclass of pseudohyperplane\nar rangements. We show that signotopes of odd rank are extendable in the\nsen se that for two prescribed crossing points we can add an element\ncontaini ng them.\n LOCATION:https://researchseminars.org/talk/ACPMS/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrien Laurent DTSTART:20240503T130000Z DTEND:20240503T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/40 DESCRIPTION:Title: O n the geometric and algebraic properties of stochastic backward error anal ysis\nby Adrien Laurent as part of Algebraic and Combinatorial Perspec tives in the Mathematical Sciences\n\n\nAbstract\nThe exotic aromatic exte nsion of Butcher series allowed the creation and study of integrators for the high-order sampling of the invariant measure of ergodic stochastic dif ferential equations. In particular\, the concept of backward error analysi s\, a key concept in geometric numerical integration\, seemed to generalis e in a certain sense for the study of stochastic dynamics using exotic aro matic B-series\, though there was no general result beyond order 3. In thi s talk\, we will detail the concept of backward error analysis\, quickly p resent recent results on the Hopf algebra structures related to the compos ition and substitution laws of exotic aromatic series\, and see that stoch astic backward error analysis writes naturally and at any order with exoti c aromatic B-series. Then\, we shall show that the exotic aromatic formali sm is precisely the right formalism for the formulation of backward error analysis\, thanks to a universal geometric property of orthogonal equivari ance. This is joint work with Eugen Bronasco (University of Geneva) and Ha ns Munthe-Kaas (University of Bergen and University of Tromsø).\n LOCATION:https://researchseminars.org/talk/ACPMS/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Cyril Banderier DTSTART:20240517T130000Z DTEND:20240517T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/41 DESCRIPTION:Title: F rom geometry to generating functions: rectangulations and permutations \nby Cyril Banderier as part of Algebraic and Combinatorial Perspectives i n the Mathematical Sciences\n\n\nAbstract\nA rectangulation of size n is a tiling of a rectangle by n rectangles such that no four rectangles meet i n a point. In the literature\, rectangulations are also called floorplans or rectangular dissections. In this talk\, we will analyse several classes of pattern-avoiding rectangulations which lead to surprisingly nice enume rative results and new bijective links with pattern-avoiding permutations. We prove that their generating functions are algebraic\, and confirm seve ral conjectures by Merino and Mütze. We also analyse a new class of rect angulations\, called whirls: they are related to Catalan numbers\, but no simple proof of it is known! We prove this fact using a generating tree. T his leads to an intricate functional equation\, for which the method of re solution has its own interest.\n LOCATION:https://researchseminars.org/talk/ACPMS/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlo Bellingeri DTSTART:20240531T130000Z DTEND:20240531T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/42 DESCRIPTION:Title: T he Euler-Maclaurin formula and generalised iterated integrals\nby Carl o Bellingeri as part of Algebraic and Combinatorial Perspectives in the Ma thematical Sciences\n\n\nAbstract\nConsidered one of the key identities in classical analysis\, the Euler-McLaurin formula is one of the standard to ols for relating sums and integrals\, with remarkable applications in many areas of mathematics\, although it is little used in stochastic analysis. In this talk\, we will show how\, by introducing new variants of the iter ated integrals of a path and a simple variational problem\, we can general ise this identity in the context of Riemann Stieltjes integration. Joint w ork with Sylvie Paycha (Potsdam) and Peter Friz (TU Berlin and WIAS)\n LOCATION:https://researchseminars.org/talk/ACPMS/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Tobias Fritz DTSTART:20240607T130000Z DTEND:20240607T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/43 DESCRIPTION:Title: S elf-distributive structures in physics\nby Tobias Fritz as part of Alg ebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\nAb stract\nIn all of our current physical theories\, it is a central feature that observables generate 1-parameter groups of transformations. For examp le\, a Hamiltonian generates time translations\, while the angular momentu m observable generates rotations. In this talk\, I will explain how this p roperty is captured algebraically by the new notion of Lie quandle. The ce ntral ingredient is a version of the self-distributivity equation $x\\rhd( y\\rhd z)=(x\\rhd y)\\rhd(x\\rhd z)$. I will argue that Lie quandles can b e thought of as nonlinear generalizations of Lie algebras. It is intriguin g that not only the observables of physical theories form a Lie quandle\; the same is true for the (mixed) states\, where the Lie quandle structure is given by the formation of probabilistic mixtures.\n LOCATION:https://researchseminars.org/talk/ACPMS/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Christine Vespa (Université d'Aix-Marseille) DTSTART:20240906T130000Z DTEND:20240906T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/44 DESCRIPTION:Title: W heeled PROP structure on stable cohomology\nby Christine Vespa (Univer sité d'Aix-Marseille) as part of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nWheeled PROPs\, introduced by Markl\, Merkulov and Shadrin are PROPs equipped with extra structures whi ch can treat traces. In this talk\, after explaining the notions of PROPs and wheeled PROPs\, I will describe a wheeled PROP structure on stable coh omology of automorphism groups of free groups with some particular coeffic ients. I will explain how cohomology classes constructed previously by Kaw azumi can be interpreted using this wheeled PROP structure and I will cons truct a morphism of wheeled PROPs from a PROP given in terms of functor ho mology and the wheeled PROP evoked previously. This is joint work with Nar iya Kawazumi.\n LOCATION:https://researchseminars.org/talk/ACPMS/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Leandro Vendramin DTSTART:20240920T130000Z DTEND:20240920T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/45 DESCRIPTION:Title: W hat is a skew brace?\nby Leandro Vendramin as part of Algebraic and Co mbinatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nThe t alk is an introduction to the theory of skew braces and their application to the\nstudy of combinatorial solutions of the Yang-Baxter equation.\n LOCATION:https://researchseminars.org/talk/ACPMS/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Dudzik DTSTART:20240628T130000Z DTEND:20240628T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/46 DESCRIPTION:by Andrew Dudzik as part of Algebraic and Combinatorial Perspe ctives in the Mathematical Sciences\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Laubie (IRMA Strasbourg) DTSTART:20250131T140000Z DTEND:20250131T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/47 DESCRIPTION:Title: V olume preservation of Butcher series methods from the operadic viewpoint\nby Paul Laubie (IRMA Strasbourg) as part of Algebraic and Combinatoria l Perspectives in the Mathematical Sciences\n\n\nAbstract\nAfter a quick i ntroduction on Butcher series methods\, we recall the theorem of Iserles-Q uispel-Tse/Chartier-Murua on the nonexistence of volume preserving Butcher series methods. We will then give some algebraic and combinatorial recoll ections on operads\, and introduce the operads and the techniques appearin g in the new proof of this theorem. If time permits\, we will explain how the operadic viewpoint also allows us to recover the full classification o f volume preserving aromatic Butcher series methods\, which was first comp uted by Laurent\, McLachlan\, Munthe-Kaas\, and Verdier.\n LOCATION:https://researchseminars.org/talk/ACPMS/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Gunnar Fløystad (University of Bergen) DTSTART:20250214T140000Z DTEND:20250214T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/48 DESCRIPTION:Title: S ubmodular functions\, generalized permutahedra\, conforming preorders\, an d cointeracting bialgebras\nby Gunnar Fløystad (University of Bergen) as part of Algebraic and Combinatorial Perspectives in the Mathematical S ciences\n\n\nAbstract\nGeneralized permutahedra (GP) is a central class of polyhedra with surprisingly many connections to various areas. Examples a re matroid polytopes and and \npolymatroids. GP are also equivalent to sub modular functions\, an\nimportant class in optimization and economics.\n\n To a submodular function we:\nDefine a class of preorders\, conforming pre orders\nWe show the faces of a GP are in bijection with the conforming pre orders.\nThe face poset structure of the GP induces two order relations on conforming preorders\, subdivision and contraction\, and we investigate t heir properties.\nThere is Hopf monoid of submodular functions. We show it has a bimonoid of modular functions cointeracting in a non-standard way. By recent theory of L.Foissy this associates a canonical polynomial to any submodular function.\n LOCATION:https://researchseminars.org/talk/ACPMS/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Khalef Yaddaden (Nagoya University) DTSTART:20250314T140000Z DTEND:20250314T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/49 DESCRIPTION:Title: S chemes of double shuffle and distribution relations among cyclotomic multi ple zeta values\nby Khalef Yaddaden (Nagoya University) as part of Alg ebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\nAb stract\nWe are interested in two formal approaches reflecting the combinat orial properties of double shuffle relations between cyclotomic multiple z eta values of level \\(N \\ge 1\\). The first approach\, introduced by Rac inet\, considers cyclotomic multiple zeta values from the perspective of t he Drinfeld associator and provides a description based on Hopf algebra co products\, which he encodes in a scheme DMR(N). The second\, studied by Ho ffmann\, Ihara-Kaneko-Zagier (\\(N=1\\))\, Arakawa-Kaneko and Zhao (\\(N \ \ge 1\\))\, describes these relations through algebra products that we enc ode in a scheme EDS(N). When \\(N > 1\\)\, the cyclotomic multiple zeta va lues of level N also satisfy distribution relations that Racinet incorpora tes into a subscheme DMRD(N) of DMR(N). In this presentation\, we establis h an isomorphism between the schemes DMR(N) and EDS(N)\, then introduce a subscheme EDSD(N) of EDS(N) that we identify with DMRD(N). This identifica tion enables us to prove a conjecture of Zhao stating that the weight 2 di stribution relations are a consequence of double shuffle relations as well as weight 1 and depth 2 distribution relations (this talk is based on a j oint work with Henrik Bachmann).\n LOCATION:https://researchseminars.org/talk/ACPMS/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Kim Jung-Wook (Albert Einstein Institute) DTSTART:20250425T130000Z DTEND:20250425T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/50 DESCRIPTION:Title: A lgebra of graphs for scattering dynamics\nby Kim Jung-Wook (Albert Ein stein Institute) as part of Algebraic and Combinatorial Perspectives in th e Mathematical Sciences\n\n\nAbstract\nFeynman diagrams are an iconic inst ance of diagrammatic tools in theoretical physics\, which were developed f or describing quantum scattering dynamics of particles in quantum field th eory. With a small modification to diagrammatic rules\, the Feynman diagra ms can be repurposed to describe classical scattering dynamics\, where roo ted tree graphs are given a special role of computing the impulse (momentu m change from scattering). I will explain how repackaging the classical sc attering dynamics as a symmetry transformation (symplectic transformation) leads to the Poisson algebra of directed tree graphs\, the Magnus series\ , and the Hopf algebra of graphs by Calaque\, Ebrahimi-Fard\, and Manchon. This talk is based on arXiv:2410.22988 [hep-th]\, a work in collaboration with Joon-Hwi Kim\, Sungsoo Kim\, and Sangmin Lee.\n LOCATION:https://researchseminars.org/talk/ACPMS/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Frédéric Patras (Université Côte d'Azur) DTSTART:20250411T130000Z DTEND:20250411T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/51 DESCRIPTION:Title: M atrix symmetric and quasi-symmetric functions\nby Frédéric Patras (U niversité Côte d'Azur) as part of Algebraic and Combinatorial Perspectiv es in the Mathematical Sciences\n\n\nAbstract\nA fundamental result by L. Solomon states that formulas for the computation of tensor products of sym metric group representations can be lifted to the corresponding (Solomon ’s) descent algebra\, a subalgebra of the group algebra with a very rich structure. Motivated by the structure of the product formula in these alg ebras and by other results and ideas in the field\, we introduce and inves tigate a two dimensional analog based on packed integer matrices that inhe rits most of their fundamental properties. One of the structures we introd uce identifies with a bialgebra recently introduced by J. Diehl and L. Sch mitz to define a two dimensional generalisation of Chen’s iterated integ rals signatures. J.w. with L. Foissy and C. Malvenuto.\n LOCATION:https://researchseminars.org/talk/ACPMS/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Loïc Foissy DTSTART:20250509T130000Z DTEND:20250509T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/52 DESCRIPTION:Title: D ouble bialgebra of noncrossing partitions\nby Loïc Foissy as part of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\ nAbstract\nA double bialgebra is a family $(A\,m\,\\Delta\,\\delta)$ such that both $(A\,m\,\\Delta)$ and $(A\,m\,\\delta)$ are bialgebras\, with th e extra condition that seeing $\\delta$ as a right coaction on itself\, $m $ and $\\Delta$ are right comodules morphism over $(A\,m\,\\delta)$. A cla ssical example is given by the polynomial algebra $\\mathbb{C}[X]$\, with its two classical coproducts. In this talk\, we will present a double bial gebra structure on the symmetric algebra generated by noncrossing partitio ns. The first coproduct is given by the separations of the blocks of the p artitions\, with respect to the entanglement\, and the second one by fusio ns of blocks. This structure implies that there exists a unique polynomial invariant on noncrossing partitions which respects both coproducts: we wi ll give some elements on this invariant\, and applications to the antipode of noncrossing partitions.\n LOCATION:https://researchseminars.org/talk/ACPMS/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentine Soto DTSTART:20250523T130000Z DTEND:20250523T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/53 DESCRIPTION:Title: G eneralized Kauer moves and derived equivalences of skew Brauer graph algeb ras\nby Valentine Soto as part of Algebraic and Combinatorial Perspect ives in the Mathematical Sciences\n\n\nAbstract\nBrauer graph algebras are finite dimensional algebras constructed from the combinatorial data of a graph called a Brauer graph. Kauer proved that derived equivalences of Bra uer graph algebras can be obtained from the move of one edge in the corres ponding Brauer graph. Moreover\, this derived equivalence is entirely desc ribed thanks to a tilting object which can be interpreted in terms of silt ing mutation. In this talk\, I will be interested in skew Brauer graph alg ebras which generalize the class of Brauer graph algebras. These algebras are constructed from the combinatorial data of a Brauer graph where some e dges might be "degenerate". I will explain how Kauer's results can be gene ralized for the move of multiple edges and to the case of skew Brauer grap h algebras.\n LOCATION:https://researchseminars.org/talk/ACPMS/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Tal Gottesman (Ruhr-Universität Bochum) DTSTART:20250606T130000Z DTEND:20250606T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/54 DESCRIPTION:Title: F ractional Calabi-Yau lattices\nby Tal Gottesman (Ruhr-Universität Boc hum) as part of Algebraic and Combinatorial Perspectives in the Mathematic al Sciences\n\n\nAbstract\nF. Chapoton made public in 2023 an intriguing c onjecture linking combinatorial formulas\, symplectic geometry\, and repr esentation theory of fractional Calabi-Yau posets. After exposing recent p rogress around this conjecture\, I shall present the fractional Calabi-Yau property for lattices and how to prove it. If time permits\, I'll conside r the poset of plane partitions\, for which the conjecture remains open\n LOCATION:https://researchseminars.org/talk/ACPMS/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcel Wack (TU Berlin) DTSTART:20251010T130000Z DTEND:20251010T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/55 DESCRIPTION:by Marcel Wack (TU Berlin) as part of Algebraic and Combinator ial Perspectives in the Mathematical Sciences\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Ulf Kühn (Universität Hamburg) DTSTART:20250620T130000Z DTEND:20250620T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/56 DESCRIPTION:Title: I nteresting coproducts through post-Lie algebras\nby Ulf Kühn (Univers ität Hamburg) as part of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nThis talk reports on joint work with Annika Burmester\, https://arxiv.org/abs/2504.19661 . We study post-Lie st ructures on free Lie algebras\, the Grossman-Larson product on their envel oping algebras\, and provide an abstract formula for its dual coproduct. T his might be of interest for the general theory of post-Hopf algebras. Usi ng a magmatic approach\, we explore post-Lie algebras connected to multipl e zeta values and their q-analogues. For multiple zeta values\, this frame work yields an algebraic interpretation of the Goncharov coproduct. Assumi ng that the Bernoulli numbers satisfy the so called threshold shuffle iden tities\, we present a post-Lie structure\, whose induced Lie bracket we ex pect to restrict to the dual of indecomposables of multiple q-zeta values. \n LOCATION:https://researchseminars.org/talk/ACPMS/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Lorenzo Clemente (University of Warsaw) DTSTART:20250919T130000Z DTEND:20250919T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/57 DESCRIPTION:Title: A lgorithmic analysis of control systems with affine input and polynomial st ate dynamics\nby Lorenzo Clemente (University of Warsaw) as part of Al gebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\nA bstract\nWe provide simple algorithms for the formal analysis of determini stic continuous-time control systems whose dynamics is affine in the input and polynomial in the state (in short\, polynomial systems). We consider the following semantic properties: input-output equivalence\, input indepe ndence\, linearity\, and analyticity. Our approach is based on Chen-Fliess series\, which provide a unique representation of the dynamics of such sy stems via their generating series (in noncommuting indeterminates). Our st arting point is Fliess' seminal work showing how the semantic properties a bove are mirrored by corresponding combinatorial properties on generating series. Next\, we observe that the generating series of polynomial systems coincide with the class of shuffle-finite series\, a nonlinear generalisa tion of Schützenberger's rational series which we have recently studied i n the context of automata theory and enumerative combinatorics. We exploit and extend recent results in the algorithmic analysis of shufflef-finite series to show that the semantic properties above are decidable for polyno mial systems.\n LOCATION:https://researchseminars.org/talk/ACPMS/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Lionni (ENS Lyon) DTSTART:20251003T130000Z DTEND:20251003T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/58 DESCRIPTION:by Luca Lionni (ENS Lyon) as part of Algebraic and Combinatori al Perspectives in the Mathematical Sciences\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Samuel Crew (National Tsing Hua University) DTSTART:20250905T130000Z DTEND:20250905T140000Z DTSTAMP:20260422T212609Z UID:ACPMS/59 DESCRIPTION:Title: Q uantum path signatures\nby Samuel Crew (National Tsing Hua University) as part of Algebraic and Combinatorial Perspectives in the Mathematical S ciences\n\n\nAbstract\nI discuss recent work on quantum path signatures th at places path signatures and associated kernels in a physical gauge-theor etic context. Specifically\, I will introduce random unitary developments of smooth paths and derive governing integro-differential that generalise loop equations from random matrix theory. I will discuss a quantum circuit construction and a sparse GUE ensemble that give rise to an efficient qua ntum algorithm in the one clean qubit model to compute the development.\n LOCATION:https://researchseminars.org/talk/ACPMS/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Razvan Gurau (Universität Heidelberg) DTSTART:20251031T140000Z DTEND:20251031T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/60 DESCRIPTION:by Razvan Gurau (Universität Heidelberg) as part of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Strunck (Evercot AI) DTSTART:20251114T140000Z DTEND:20251114T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/61 DESCRIPTION:by Alexander Strunck (Evercot AI) as part of Algebraic and Com binatorial Perspectives in the Mathematical Sciences\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ACPMS/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudia Fevola (MATHEXP INRIA Saclay) DTSTART:20251128T140000Z DTEND:20251128T150000Z DTSTAMP:20260422T212609Z UID:ACPMS/62 DESCRIPTION:by Claudia Fevola (MATHEXP INRIA Saclay) as part of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\nAbstract: T BA\n LOCATION:https://researchseminars.org/talk/ACPMS/62/ END:VEVENT END:VCALENDAR