BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Rebecca R.G. (George Mason University) DTSTART:20261023T193000Z DTEND:20261023T203000Z DTSTAMP:20261023T074809Z UID:MAAGC2026/1 DESCRIPTION:Title: Applications of algebra\, geometry\, and combinatorics to spatial navigation\nby Rebecca R.G. (George Mason University) as part of MAAG C 2026\n\nLecture held in Temple 1169.\n\nAbstract\nThere are three types of cells involved in spatial navigation: place cells\, grid cells\, and he ad direction cells. Place cells fire every time an animal is in a specific location\, grid cells fire in a repeating sequence as the animal travels along particular trajectories\, and head direction cells indicate the way an animal is facing. While many people study these using mathematical mode ling and more traditional applied mathematics techniques\, there is a grow ing community of people using algebraic\, geometric\, and combinatorial to ols to analyze place and grid cells. In this talk I'll discuss how I use c ombinatorial commutative algebra to study place cells (building on work of Curto\, Itskov\, et al) and geometry to study grid cells. The work on pla ce cells is joint with Hugh Geller\, Alexandra Seceleanu\, and Nora Youngs \, and the work on grid cells is joint with Giorgio Ascoli\, Holger Dannen berg\, Kelsi Listman\, Nate Sutton\, and Anthony Vu.\n LOCATION:/talk/MAAGC2026/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Brendon Rhoades (University of California\, San Diego) DTSTART:20261023T213000Z DTEND:20261023T223000Z DTSTAMP:20261023T074809Z UID:MAAGC2026/2 DESCRIPTION:Title: Coinvariants\, hyperplanes\, and superspace\nby Brendon Rhoad es (University of California\, San Diego) as part of MAAGC 2026\n\nLecture held in Temple 1169.\n\nAbstract\nLet V be a finite-dimension vector spac e. The superspace ring associated to V is the tensor product \\Omega of th e ring S of polynomial functions on V with the exterior algebra E over V. If G is any subgroup of GL(V)\, there is a natural bigraded action of G on \\Omega\, and the superspace coinvariant ring SR_G is obtained by quotien ting \\Omega by the ideal generated by G-invariants with vanishing constan t term. We study the structure of SR_G when G is a complex reflection grou p and V is its reflection representation with a special focus on type A. T he theory of hyperplane arrangements plays an important role. Joint with R obert Anarone\, Sutanay Bhattacharya\, Patty Commins\, Trevor Karn\, Satos hi Murai\, and Andy Wilson.\n LOCATION:/talk/MAAGC2026/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonardo Mihalcea (Virginia Tech) DTSTART:20261024T140000Z DTEND:20261024T150000Z DTSTAMP:20261023T074809Z UID:MAAGC2026/3 DESCRIPTION:Title: Quantum Schubert Calculus from lattice models\nby Leonardo Mi halcea (Virginia Tech) as part of MAAGC 2026\n\nLecture held in Temple 116 9.\n\nAbstract\nQuantum Schubert Calculus arises from questions in Enumera tive Geometry\, such as how many rational curves of a specified degree int ersect general translates of Schubert varieties in a Grassmannian. The ans wer may be found by calculating the structure constants of the multiplicat ion of Schubert classes in an appropriate quantum intersection ring associ ated to a Grassmann manifold. I will explain how techniques from statistic al mechanics\, namely the combinatorics of partition functions of certain lattice models\, yield explicit combinatorial formulae for the Schubert st ructure constants. Joint work with V. Gorbounov and C. Korff.\n LOCATION:/talk/MAAGC2026/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Josef Svoboda (Caltech) DTSTART:20261024T160000Z DTEND:20261024T170000Z DTSTAMP:20261023T074809Z UID:MAAGC2026/4 DESCRIPTION:Title: Brieskorn homology 3-spheres\, GL(2\,Z) and the Stern—Brocot tr ee\nby Josef Svoboda (Caltech) as part of MAAGC 2026\n\nLecture held i n Temple 1169.\n\nAbstract\nThe d-invariant of a homology sphere $\\Sigma( p\,q\,r)$ is a non-negative integer. It obstructs the existence of smooth contractible 4-manifolds with the boundary $\\Sigma(p\,q\,r)$. By a resul t of Elkies\, d vanishes exactly when the corresponding resolution (or plu mbing) lattice is diagonalizable. We completely characterize Brieskorn sph eres $Sigma(2\,q\,r)$ with d=0\, using the combinatorics of Stern—Brocot tree and free submonoids of GL(2\,Z). Joint work with Shimal Harichurn\, Isabella Khan and András Némethi.\n LOCATION:/talk/MAAGC2026/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergi Elizalde (Dartmouth College) DTSTART:20261025T140000Z DTEND:20261025T150000Z DTSTAMP:20261023T074809Z UID:MAAGC2026/5 DESCRIPTION:Title: Cylindric growth diagrams\, walks in simplices\, and exclusion pr ocesses\nby Sergi Elizalde (Dartmouth College) as part of MAAGC 2026\n \nLecture held in Temple 1169.\n\nAbstract\nWe establish bijections betwee n three classes of combinatorial objects that have been studied in differe nt contexts: lattice walks in simplicial regions as introduced by Mortimer --Prellberg\, standard cylindric tableaux as introduced by Gessel--Kratten thaler and Postnikov\, and sequences of states in the totally asymmetric s imple exclusion process on a cycle. This perspective allows us to translat e symmetries from one setting into another\, revealing unexpected properti es of these objects.\nSpecifically\, we show that a recent bijection of Co urtiel et al. between certain simplicial walks with forward and backward s teps is equivalent to a cylindric analogue of the Robinson--Schensted corr espondence. Originally defined by Neyman by iterating an insertion operati on\, we provide an alternative description of this correspondence by intro ducing a cylindric version of Fomin's growth diagrams. This natural descri ption elucidates the symmetry of the correspondence\, and it allows us to interpret the above walks as oscillating cylindric tableaux.\n LOCATION:/talk/MAAGC2026/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Bridger Tenner (DePaul University) DTSTART:20261025T153000Z DTEND:20261025T163000Z DTSTAMP:20261023T074809Z UID:MAAGC2026/6 DESCRIPTION:Title: Permutation Patterns: TNG\nby Bridger Tenner (DePaul Universi ty) as part of MAAGC 2026\n\nLecture held in Temple 1169.\n\nAbstract\nPer mutations are a classic tool for modeling a variety of scenarios. The stud y of permutations in their own right\, as combinatorial objects\, has blos somed in the last half century through a burgeoning interest in permutatio n patterns. The patterns that a given permutation contains (or avoids) hav e shown remarkable relevance - and with applications to numerous other fie lds. We will discuss major themes of that research\, as well as exciting a nd relatively new directions for the field. These directions\, sometimes c omplementary to classical results\, have already shown great utility and a re poised for even more\, suggesting a thrilling new generation of researc h to come. Including collaborations with Yosef Berman\, Ian Cavey & Hugh D ennin\, Joel Lewis\, and Kyle Petersen.\n LOCATION:/talk/MAAGC2026/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Martha Yip (University of Kentucky) DTSTART:20261025T170000Z DTEND:20261025T180000Z DTSTAMP:20261023T074809Z UID:MAAGC2026/7 DESCRIPTION:Title: Flag positroid pipe dreams\nby Martha Yip (University of Kent ucky) as part of MAAGC 2026\n\nLecture held in Temple 1169.\n\nAbstract\nW e introduce flag positroid pipe dreams (FPPs)\, whose role in the study of complete flag positroids is analogous to the role of Le-diagrams in the s tudy of positroids. FPPs are in bijection with intervals in the Bruhat ord er and hence index Richardson cells in the decomposition of the nonnegativ e flag variety. In this talk\, we will show how a flag positroid can be bu ilt rank by rank via FPPs\, and conversely given an FPP\, how to recover t he constituents of its associated complete flag positroid in terms of thei r Le-diagrams. As an application\, we address a problem posed by Chen et a l. regarding a characterization of elementary positroid quotients via the cyclic shift operators of Benedetti et al.\n LOCATION:/talk/MAAGC2026/7/ END:VEVENT END:VCALENDAR