BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Melissa Chiu-Chu Liu (Columbia University) DTSTART:20240812T170000Z DTEND:20240812T180000Z DTSTAMP:20260422T212937Z UID:RVAGeometry2024/1 DESCRIPTION:Title: Mirror symmetry for theta divisors\nby Melissa Chiu-Chu Liu (C olumbia University) as part of Richmond Geometry Meeting 2024\n\nLecture h eld in Room 1169 in the Temple building.\n\nAbstract\nI will describe a ve rsion of global Strominger-Yau-Zaslow (SYZ) mirror symmetry and homologica l mirror symmetry for a theta divisor in a principally polarized abelian v ariety of any dimension\, over the complex moduli of principally polarized and SYZ fibered abelian varieties. This is based on joint work with Haniy a Azam\, Catherine Cannizzo\, and Heather Lee.\n LOCATION:https://researchseminars.org/talk/RVAGeometry2024/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Scott Baldridge (Louisiana State University) DTSTART:20240812T190000Z DTEND:20240812T200000Z DTSTAMP:20260422T212937Z UID:RVAGeometry2024/2 DESCRIPTION:Title: From Gromov-Witten Theory to the Four Color Theorem\nby Scott Baldridge (Louisiana State University) as part of Richmond Geometry Meetin g 2024\n\nLecture held in Room 1169 in the Temple building.\n\nAbstract\nG romov-Witten theory is the study of pseudoholomorphic curves\, i.e.\, maps of genus $g$ Riemann surfaces with $n$ marked points into a symplectic ma nifold $Y$. If the manifold $Y$ is also foliated generically by special La grangian tori\, i.e.\, the SYZ conjecture\, then one can study the moduli space of pseudoholomorphic maps of genus $g$ Riemann surfaces with measure d foliations into $Y$ that preserve the foliations.\n\nRiemann surfaces wi th measured foliations have long been known to correspond to metric ribbon graphs\, i.e.\, special CW structures of a surface where marked points co rrespond to $2$-cells and each edge of the graph has a positive number ass ociated to it (the metric). The moduli space of genus $g$ Riemann surface s with measured foliations is a well-behaved orbifold whose points are gen erically given by trivalent ribbon graphs with $n$ faces. \n\nMotivated by this background we ask: For foliated spheres with $n$ marked points\, can the marked points ($2$-cells) in GW Theory be painted with four colors so that no two "adjacent" marked points have the same color? In this talk\, we generate vector spaces from diagrams (that should be reminiscent of Kho vanov homology) of a ribbon graph and define a differential between them b ased on a Frobenius algebra. We show that the dimension of the kernel of t his differential is equal to the number of ways to four-face color the gra ph (the Four Color Theorem). We then generalize this calculation to a homo logy theory based upon a topological quantum field theory. The diagrams ge nerated from the graph represent the possible quantum states of the CW str ucture of the sphere and the homology is\, in some sense\, the vacuum expe ctation value of this system. It gets wickedly complicated from this point on\, but I hope to leave you wondering: Is the four color theorem just an extremely-difficult-to-prove oddity in graph theory\, or is it tied in so me fundamental way to the deeper laws of nature and space?\n\nBelieve it o r not\, this talk will be hands-on and the ideas will be explained through the calculation of easy examples! My goal is to attract students and math ematicians to this area by making the ideas as intuitive as possible.\n LOCATION:https://researchseminars.org/talk/RVAGeometry2024/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Ross Akhmechet (Columbia University) DTSTART:20240812T210000Z DTEND:20240812T220000Z DTSTAMP:20260422T212937Z UID:RVAGeometry2024/3 DESCRIPTION:Title: Lattice homology and q-series invariants of 3-manifolds\nby Ro ss Akhmechet (Columbia University) as part of Richmond Geometry Meeting 20 24\n\nLecture held in Room 1169 in the Temple building.\n\nAbstract\nI wil l discuss joint work with Peter Johnson and Slava Krushkal that unifies an d extends two invariants of negative definite plumbed 3-manifolds: lattice homology\, due to Némethi\, which is isomorphic to Heegaard Floer homolo gy\, and the Gukov-Pei-Putrov-Vafa Z-hat q-series\, which recovers WRT qua ntum invariants. Both theories have extensions to plumbed knot complements \, and I will also discuss joint work with Peter Johnson and Sunghyuk Park in the knot complement setting\, including a surgery formula.\n LOCATION:https://researchseminars.org/talk/RVAGeometry2024/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Burt Totaro (UCLA) DTSTART:20240813T130000Z DTEND:20240813T140000Z DTSTAMP:20260422T212937Z UID:RVAGeometry2024/4 DESCRIPTION:Title: Algebraic varieties at the extremes\nby Burt Totaro (UCLA) as part of Richmond Geometry Meeting 2024\n\nLecture held in Room 1169 in the Temple building.\n\nAbstract\nIn trying to classify algebraic varieties\, there is a particular fascination in trying to construct varieties with e xtreme behavior. For example\, try to find Calabi-Yau varieties with large Betti numbers\, or varieties of general type with many vanishing plurigen era. We construct varieties with doubly exponential behavior for several s uch problems. Some of these examples are conjecturally optimal. (Joint wit h Louis Esser and Chengxi Wang.)\n LOCATION:https://researchseminars.org/talk/RVAGeometry2024/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Caner Nazaroglu (University of Cologne\, Germany) DTSTART:20240813T150000Z DTEND:20240813T160000Z DTSTAMP:20260422T212937Z UID:RVAGeometry2024/5 DESCRIPTION:Title: Constructions and Applications of Mock Modularity at Depth Two \nby Caner Nazaroglu (University of Cologne\, Germany) as part of Richmond Geometry Meeting 2024\n\nLecture held in Room 1169 in the Temple building .\n\nAbstract\nFalse and mock modular forms along with their higher depth generalizations make their appearance in mathematical physics and geometry in contexts such as Vafa-Witten invariants or Z-hat invariants of three m anifolds. In this talk I will describe the interaction between various con structions of these objects and their Fourier coefficients by focusing on a particular example involving rank 2 Vafa-Witten invariants. In particula r\, I will demonstrate a Hardy-Ramanujan-Rademacher type exact formulae fo r these Vafa-Witten invariants along with a twofold Eisenstein series cons truction for the pure component of the generating function. In particular\ , the latter construction leads to nontrivial identities for the Fourier c oefficients of the aforementioned depth two mock modular forms\, which hav e expressions as indefinite theta series derived from the wall-crossing fo rmula. This is based on earlier as well as ongoing work with K. Bringmann. \n LOCATION:https://researchseminars.org/talk/RVAGeometry2024/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Shashank Kanade (University of Denver) DTSTART:20240813T180000Z DTEND:20240813T190000Z DTSTAMP:20260422T212937Z UID:RVAGeometry2024/6 DESCRIPTION:Title: Torus knots and characters of vertex operator algebras\nby Sha shank Kanade (University of Denver) as part of Richmond Geometry Meeting 2 024\n\nLecture held in Room 1169 in the Temple building.\n\nAbstract\nI wi ll explain how invariants of torus knots\, coloured with representations o f a finite-dimensional simply-laced Lie algebra $\\mathfrak{g}$ lead to ch aracters of the corresponding principal $W$-algebra (which is a kind of ve rtex operator algebra). This relationship rests on a conjecture about asym ptotic weight multiplicities in finite-dimensional irreducible $\\mathfrak {g}$-modules.\n LOCATION:https://researchseminars.org/talk/RVAGeometry2024/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicola Pagani (Univertsity of Liverpool\, UK) DTSTART:20240814T130000Z DTEND:20240814T140000Z DTSTAMP:20260422T212937Z UID:RVAGeometry2024/7 DESCRIPTION:Title: Classification of compactified Jacobians over nodal curves\nby Nicola Pagani (Univertsity of Liverpool\, UK) as part of Richmond Geometr y Meeting 2024\n\nLecture held in Room 1169 in the Temple building.\n\nAbs tract\nIf X is a smooth proper curve\, then the Jacobian of X is a classic al and well-studied object in algebraic geometry. When X is singular\, the moduli space of degree 0 line bundles is rarely compact\, and over the la st century many efforts have been made to study the modular compactificati ons of this space\, which we call "compactified Jacobians of X". In this t alk we focus on the case when X has at worst nodal singularities. Some com pactified Jacobians cannot arise as limits of Jacobians of smooth curves - we regard them as exotic objects. We will see that\, if one excludes thes e exotic cases\, then one can give a simple and complete combinatorial cla ssification of all compactified Jacobians. This is based on work of myself with Tommasi\, on a paper by Viviani\, and on work in progress with Fava and Viviani.\n LOCATION:https://researchseminars.org/talk/RVAGeometry2024/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Sunghyuk Park (Harvard University) DTSTART:20240814T143000Z DTEND:20240814T153000Z DTSTAMP:20260422T212937Z UID:RVAGeometry2024/8 DESCRIPTION:Title: 3-manifolds and q-series\nby Sunghyuk Park (Harvard University ) as part of Richmond Geometry Meeting 2024\n\nLecture held in Room 1169 i n the Temple building.\n\nAbstract\nThis is a gentle introduction to the Z -hat invariant\, which assigns interesting q-series to 3-manifolds decorat ed by spin^c structures.\n LOCATION:https://researchseminars.org/talk/RVAGeometry2024/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Danielle O'Donnol (Marymount University) DTSTART:20240814T160000Z DTEND:20240814T170000Z DTSTAMP:20260422T212937Z UID:RVAGeometry2024/9 DESCRIPTION:Title: Theta-curves with unknotting number 1\nby Danielle O'Donnol (M arymount University) as part of Richmond Geometry Meeting 2024\n\nLecture held in Room 1169 in the Temple building.\n\nAbstract\nMotivated by the kn otting and unknotting that can occur in biological structures like DNA and proteins\, we examined when theta-curves (and knotoids) have unknotting n umber one. In collaboration with Ken Baker\, Dorothy Buck\, Allison Moore \, and Scott Taylor\, I have shown that unknotting number one theta-curves are prime. This is an extension of Scharlemann's theorem that all unknot ting number one knots are prime. Initially one might expect the version f or theta-curves to follow easily from Scharlemann’s theorem\, but the si tuation is more subtle. In this talk I will discuss this result.\n LOCATION:https://researchseminars.org/talk/RVAGeometry2024/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Welcome Message DTSTART:20240812T164500Z DTEND:20240812T170000Z DTSTAMP:20260422T212937Z UID:RVAGeometry2024/10 DESCRIPTION:Title: Welcome Message\nby Welcome Message as part of Richmond Geome try Meeting 2024\n\nLecture held in VCU Temple 1169.\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/RVAGeometry2024/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Career Panel DTSTART:20240813T193000Z DTEND:20240813T210000Z DTSTAMP:20260422T212937Z UID:RVAGeometry2024/11 DESCRIPTION:Title: Career Panel\nby Career Panel as part of Richmond Geometry Me eting 2024\n\nLecture held in VCU Temple 1169.\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/RVAGeometry2024/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Poster Session DTSTART:20240813T213000Z DTEND:20240813T230000Z DTSTAMP:20260422T212937Z UID:RVAGeometry2024/12 DESCRIPTION:Title: Poster Session\nby Poster Session as part of Richmond Geometr y Meeting 2024\n\nLecture held in VCU Temple 1169.\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/RVAGeometry2024/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Social Event DTSTART:20240813T234500Z DTEND:20240814T013000Z DTSTAMP:20260422T212937Z UID:RVAGeometry2024/13 DESCRIPTION:Title: Social Event\nby Social Event as part of Richmond Geometry Me eting 2024\n\nLecture held in VCU Temple 1169.\n\nAbstract\nSocial Event a t Brambly Park in Richmond\, VA: https://www.bramblypark.com/\n LOCATION:https://researchseminars.org/talk/RVAGeometry2024/13/ END:VEVENT END:VCALENDAR