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:20260404T094753Z UID:RVAGeometry2024/1 DESCRIPTION:Title: Mirror symmetry for theta divisors\nby Melissa Chiu-Chu Liu (Columbia University) as part of Richmond Geometry Meeting 2024\n\nLe cture held in Room 1169 in the Temple building.\n\nAbstract\nI will descri be a version of global Strominger-Yau-Zaslow (SYZ) mirror symmetry and hom ological mirror symmetry for a theta divisor in a principally polarized ab elian variety of any dimension\, over the complex moduli of principally po larized and SYZ fibered abelian varieties. This is based on joint work wit h Haniya Azam\, Catherine Cannizzo\, and Heather Lee.\n LOCATION:https://stable.researchseminars.org/talk/RVAGeometry2024/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Scott Baldridge (Louisiana State University) DTSTART:20240812T190000Z DTEND:20240812T200000Z DTSTAMP:20260404T094753Z 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 Meeting 2024\n\nLecture held in Room 1169 in the Temple building.\n\nAbst ract\nGromov-Witten theory is the study of pseudoholomorphic curves\, i.e. \, maps of genus $g$ Riemann surfaces with $n$ marked points into a symple ctic manifold $Y$. If the manifold $Y$ is also foliated generically by spe cial Lagrangian tori\, i.e.\, the SYZ conjecture\, then one can study the moduli space of pseudoholomorphic maps of genus $g$ Riemann surfaces with measured foliations into $Y$ that preserve the foliations.\n\nRiemann surf aces with measured foliations have long been known to correspond to metric ribbon graphs\, i.e.\, special CW structures of a surface where marked po ints correspond to $2$-cells and each edge of the graph has a positive num ber associated to it (the metric). The moduli space of genus $g$ Riemann surfaces with measured foliations is a well-behaved orbifold whose points are generically given by trivalent ribbon graphs with $n$ faces. \n\nMotiv ated by this background we ask: For foliated spheres with $n$ marked point s\, can the marked points ($2$-cells) in GW Theory be painted with four co lors 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 Khovanov homology) of a ribbon graph and define a differential between them based on a Frobenius algebra. We show that the dimension of the kern el of this differential is equal to the number of ways to four-face color the graph (the Four Color Theorem). We then generalize this calculation to a homology theory based upon a topological quantum field theory. The diag rams generated from the graph represent the possible quantum states of the CW structure of the sphere and the homology is\, in some sense\, the vacu um expectation value of this system. It gets wickedly complicated from thi s 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 tie d in some fundamental way to the deeper laws of nature and space?\n\nBelie ve it or 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 a nd mathematicians to this area by making the ideas as intuitive as possibl e.\n LOCATION:https://stable.researchseminars.org/talk/RVAGeometry2024/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Ross Akhmechet (Columbia University) DTSTART:20240812T210000Z DTEND:20240812T220000Z DTSTAMP:20260404T094753Z UID:RVAGeometry2024/3 DESCRIPTION:Title: Lattice homology and q-series invariants of 3-manifolds \nby Ross Akhmechet (Columbia University) as part of Richmond Geometry Mee ting 2024\n\nLecture held in Room 1169 in the Temple building.\n\nAbstract \nI will discuss joint work with Peter Johnson and Slava Krushkal that uni fies and extends two invariants of negative definite plumbed 3-manifolds: lattice homology\, due to Némethi\, which is isomorphic to Heegaard Floer homology\, and the Gukov-Pei-Putrov-Vafa Z-hat q-series\, which recovers WRT quantum invariants. Both theories have extensions to plumbed knot comp lements\, and I will also discuss joint work with Peter Johnson and Sunghy uk Park in the knot complement setting\, including a surgery formula.\n LOCATION:https://stable.researchseminars.org/talk/RVAGeometry2024/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Burt Totaro (UCLA) DTSTART:20240813T130000Z DTEND:20240813T140000Z DTSTAMP:20260404T094753Z UID:RVAGeometry2024/4 DESCRIPTION:Title: Algebraic varieties at the extremes\nby Burt Totaro (UC LA) as part of Richmond Geometry Meeting 2024\n\nLecture held in Room 1169 in the Temple building.\n\nAbstract\nIn trying to classify algebraic vari eties\, there is a particular fascination in trying to construct varieties with extreme behavior. For example\, try to find Calabi-Yau varieties wit h large Betti numbers\, or varieties of general type with many vanishing p lurigenera. We construct varieties with doubly exponential behavior for se veral such problems. Some of these examples are conjecturally optimal. (Jo int with Louis Esser and Chengxi Wang.)\n LOCATION:https://stable.researchseminars.org/talk/RVAGeometry2024/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Caner Nazaroglu (University of Cologne\, Germany) DTSTART:20240813T150000Z DTEND:20240813T160000Z DTSTAMP:20260404T094753Z UID:RVAGeometry2024/5 DESCRIPTION:Title: Constructions and Applications of Mock Modularity at Depth Two\nby Caner Nazaroglu (University of Cologne\, Germany) as part of R ichmond Geometry Meeting 2024\n\nLecture held in Room 1169 in the Temple b uilding.\n\nAbstract\nFalse and mock modular forms along with their higher depth generalizations make their appearance in mathematical physics and g eometry in contexts such as Vafa-Witten invariants or Z-hat invariants of three manifolds. In this talk I will describe the interaction between vari ous constructions of these objects and their Fourier coefficients by focus ing on a particular example involving rank 2 Vafa-Witten invariants. In pa rticular\, I will demonstrate a Hardy-Ramanujan-Rademacher type exact form ulae for these Vafa-Witten invariants along with a twofold Eisenstein seri es construction for the pure component of the generating function. In part icular\, the latter construction leads to nontrivial identities for the Fo urier coefficients of the aforementioned depth two mock modular forms\, wh ich have expressions as indefinite theta series derived from the wall-cros sing formula. This is based on earlier as well as ongoing work with K. Bri ngmann.\n LOCATION:https://stable.researchseminars.org/talk/RVAGeometry2024/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Shashank Kanade (University of Denver) DTSTART:20240813T180000Z DTEND:20240813T190000Z DTSTAMP:20260404T094753Z UID:RVAGeometry2024/6 DESCRIPTION:Title: Torus knots and characters of vertex operator algebras\ nby Shashank Kanade (University of Denver) as part of Richmond Geometry Me eting 2024\n\nLecture held in Room 1169 in the Temple building.\n\nAbstrac t\nI will explain how invariants of torus knots\, coloured with representa tions of a finite-dimensional simply-laced Lie algebra $\\mathfrak{g}$ lea d to characters of the corresponding principal $W$-algebra (which is a kin d of vertex operator algebra). This relationship rests on a conjecture abo ut asymptotic weight multiplicities in finite-dimensional irreducible $\\m athfrak{g}$-modules.\n LOCATION:https://stable.researchseminars.org/talk/RVAGeometry2024/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicola Pagani (Univertsity of Liverpool\, UK) DTSTART:20240814T130000Z DTEND:20240814T140000Z DTSTAMP:20260404T094753Z UID:RVAGeometry2024/7 DESCRIPTION:Title: Classification of compactified Jacobians over nodal curves< /a>\nby Nicola Pagani (Univertsity of Liverpool\, UK) as part of Richmond Geometry Meeting 2024\n\nLecture held in Room 1169 in the Temple building. \n\nAbstract\nIf X is a smooth proper curve\, then the Jacobian of X is a classical and well-studied object in algebraic geometry. When X is singula r\, the moduli space of degree 0 line bundles is rarely compact\, and over the last century many efforts have been made to study the modular compact ifications of this space\, which we call "compactified Jacobians of X". In this talk we focus on the case when X has at worst nodal singularities. S ome compactified Jacobians cannot arise as limits of Jacobians of smooth c urves - we regard them as exotic objects. We will see that\, if one exclud es these exotic cases\, then one can give a simple and complete combinator ial classification of all compactified Jacobians. This is based on work of myself with Tommasi\, on a paper by Viviani\, and on work in progress wit h Fava and Viviani.\n LOCATION:https://stable.researchseminars.org/talk/RVAGeometry2024/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Sunghyuk Park (Harvard University) DTSTART:20240814T143000Z DTEND:20240814T153000Z DTSTAMP:20260404T094753Z UID:RVAGeometry2024/8 DESCRIPTION:Title: 3-manifolds and q-series\nby Sunghyuk Park (Harvard Uni versity) as part of Richmond Geometry Meeting 2024\n\nLecture held in Room 1169 in the Temple building.\n\nAbstract\nThis is a gentle introduction t o the Z-hat invariant\, which assigns interesting q-series to 3-manifolds decorated by spin^c structures.\n LOCATION:https://stable.researchseminars.org/talk/RVAGeometry2024/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Danielle O'Donnol (Marymount University) DTSTART:20240814T160000Z DTEND:20240814T170000Z DTSTAMP:20260404T094753Z UID:RVAGeometry2024/9 DESCRIPTION:Title: Theta-curves with unknotting number 1\nby Danielle O'Do nnol (Marymount University) as part of Richmond Geometry Meeting 2024\n\nL ecture held in Room 1169 in the Temple building.\n\nAbstract\nMotivated by the knotting and unknotting that can occur in biological structures like DNA and proteins\, we examined when theta-curves (and knotoids) have unkno tting number one. In collaboration with Ken Baker\, Dorothy Buck\, Alliso n 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 unknotting number one knots are prime. Initially one might expect the ve rsion for theta-curves to follow easily from Scharlemann’s theorem\, but the situation is more subtle. In this talk I will discuss this result.\n LOCATION:https://stable.researchseminars.org/talk/RVAGeometry2024/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Welcome Message DTSTART:20240812T164500Z DTEND:20240812T170000Z DTSTAMP:20260404T094753Z UID:RVAGeometry2024/10 DESCRIPTION:Title: Welcome Message\nby Welcome Message as part of Richmon d Geometry Meeting 2024\n\nLecture held in VCU Temple 1169.\nAbstract: TBA \n LOCATION:https://stable.researchseminars.org/talk/RVAGeometry2024/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Career Panel DTSTART:20240813T193000Z DTEND:20240813T210000Z DTSTAMP:20260404T094753Z UID:RVAGeometry2024/11 DESCRIPTION:Title: Career Panel\nby Career Panel as part of Richmond Geom etry Meeting 2024\n\nLecture held in VCU Temple 1169.\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/RVAGeometry2024/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Poster Session DTSTART:20240813T213000Z DTEND:20240813T230000Z DTSTAMP:20260404T094753Z UID:RVAGeometry2024/12 DESCRIPTION:Title: Poster Session\nby Poster Session as part of Richmond Geometry Meeting 2024\n\nLecture held in VCU Temple 1169.\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/RVAGeometry2024/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Social Event DTSTART:20240813T234500Z DTEND:20240814T013000Z DTSTAMP:20260404T094753Z UID:RVAGeometry2024/13 DESCRIPTION:Title: Social Event\nby Social Event as part of Richmond Geom etry Meeting 2024\n\nLecture held in VCU Temple 1169.\n\nAbstract\nSocial Event at Brambly Park in Richmond\, VA: https://www.bramblypark.com/\n LOCATION:https://stable.researchseminars.org/talk/RVAGeometry2024/13/ END:VEVENT END:VCALENDAR