BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Topology and Geometry Seminar//EN
CALSCALE:GREGORIAN
X-WR-CALNAME:Topology and Geometry Seminar
BEGIN:VEVENT
UID:RSS-1@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20250827T103000Z
DTEND:20250827T113000Z
SUMMARY:Overview of Some Concepts Related to Compact Kähler Manifolds (Prerequisites)
DESCRIPTION:Speaker: Rajas Sandeep Sompurkar\nIn this introductory talk we will briefly review the theory of complex manifolds and almost complex structures with a few standard examples. We will then introduce the notion of a Kähler manifold and see the relevance and importance of this notion. Things like the Chern connection on a compact Kähler manifold and the resultant notion of curvature will be explained briefly with the relevant mathematical expressions. Most notably we will discuss about the Ricci and scalar curvatures and the related notion of the first Chern class of a compact Kähler manifold. The notation and conventions for the rest of the series of talks will be set in this talk.\n\nhttps://topogeoiiitd.github.io/series/existence-of-higher-extremal-kahler-metrics-on-minimal-ruled-surface/#RSS-1
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/existence-of-higher-extremal-kahler-metrics-on-minimal-ruled-surface/#RSS-1
END:VEVENT
BEGIN:VEVENT
UID:RSS-2@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20250903T090000Z
DTEND:20250903T100000Z
SUMMARY:Overview of Some Concepts Related to Holomorphic Line Bundles (Prerequisites)
DESCRIPTION:Speaker: Rajas Sandeep Sompurkar\nIn this talk we will see the definition of a holomorphic vector bundle on a compact Kähler manifold and we will also see some of the properties of it. For the purpose of this series of talks we would be mostly interested in holomorphic line bundles (which are just rank one holomorphic vector bundles)\, but we will still see some standard examples like the holomorphic tangent and cotangent bundles and most importantly for us the canonical and anticanonical line bundles associated to any compact Kähler manifold. The notions of Ricci and scalar curvature for a compact Kähler manifold introduced in the previous talk will be reformulated here in terms of the curvature of the anticanonical line bundle.\n\nhttps://topogeoiiitd.github.io/series/existence-of-higher-extremal-kahler-metrics-on-minimal-ruled-surface/#RSS-2
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/existence-of-higher-extremal-kahler-metrics-on-minimal-ruled-surface/#RSS-2
END:VEVENT
BEGIN:VEVENT
UID:RSS-3@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20250910T090000Z
DTEND:20250910T100000Z
SUMMARY:Existence of Higher Extremal Kähler Metrics on a Minimal Ruled Surface (Final Main Talk)
DESCRIPTION:Speaker: Rajas Sandeep Sompurkar\nIn this final talk our goal is to state the main results of the above mentioned research work. We will discuss about the various notions of canonical Kähler metrics on a compact Kähler manifold. These are roughly speaking Kähler metrics that satisfy some special curvature properties\, and the three well-known and well-studied notions of canonical Kähler metrics are Kähler-Einstein metrics\, constant scalar curvature Kähler (cscK) metrics and Calabi’s extremal Kähler metrics. We will define motivated by analogy the notions of higher cscK and higher extremal Kähler metrics introduced by Pingali\, which are the main objects of study in our research work. We will give a brief description of the momentum construction method of Hwang-Singer which is used in our problem of finding explicit examples of higher extremal Kähler metrics. We will set this problem in its correct context and provide the relevant references for the same.\n\nhttps://topogeoiiitd.github.io/series/existence-of-higher-extremal-kahler-metrics-on-minimal-ruled-surface/#RSS-3
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/existence-of-higher-extremal-kahler-metrics-on-minimal-ruled-surface/#RSS-3
END:VEVENT
BEGIN:VEVENT
UID:OC-1@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20250917T113000Z
DTEND:20250917T123000Z
SUMMARY:Poisson manifolds and Hamiltonian systems
DESCRIPTION:Speaker: Oscar Cosserat\nWe define Poisson manifolds and review the notions we need for this lecture : Hamiltonian vector fields\, first integrals\, Casimir functions\, symplectic foliation... The end of this first lecture is devoted to explain why traditional numerical tools do not straightforwardly apply to Hamiltonian systems on Poisson manifolds.\n\nhttps://topogeoiiitd.github.io/series/invariant-theory-of-hamiltonian-mechanics-and-related-numerical-analysis/#OC-1
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/invariant-theory-of-hamiltonian-mechanics-and-related-numerical-analysis/#OC-1
END:VEVENT
BEGIN:VEVENT
UID:OC-2@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20250924T113000Z
DTEND:20250924T123000Z
SUMMARY:Symplectic groupoids and Hamilton-Jacobi equation
DESCRIPTION:Speaker: Oscar Cosserat\nWe start by defining groupoids and relate them to Poisson manifolds through the concept of symplectic groupoid. Geometrical tools such as Lagrangian bisections will be defined and explained. In the last part of this session\, we introduce so-called "bi-realisations". Those are local forms of symplectic groupoids. On bi-realisations\, we will explain how a Hamilton-Jacobi allows to approximate Hamiltonian dynamics on Poisson manifolds.\n\nhttps://topogeoiiitd.github.io/series/invariant-theory-of-hamiltonian-mechanics-and-related-numerical-analysis/#OC-2
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/invariant-theory-of-hamiltonian-mechanics-and-related-numerical-analysis/#OC-2
END:VEVENT
BEGIN:VEVENT
UID:OC-3@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20251001T113000Z
DTEND:20251001T123000Z
SUMMARY:Hamiltonian Poisson integrator
DESCRIPTION:Speaker: Oscar Cosserat\nTo finish\, we will introduce pre-Lie algebras to solve Hamilton-Jacobi equation at arbitrary order and obtain Poisson integrators discretising Hamiltonian dynamics in that way. Geometric properties will be gathered and explained. This last session contains numerical simulations on concrete examples such as Lotka-Volterra systems and rigid body dynamics. To conclude\, we will summarize the results of this geometric approach to numerical analysis and give several perspectives.\n\nhttps://topogeoiiitd.github.io/series/invariant-theory-of-hamiltonian-mechanics-and-related-numerical-analysis/#OC-3
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/invariant-theory-of-hamiltonian-mechanics-and-related-numerical-analysis/#OC-3
END:VEVENT
BEGIN:VEVENT
UID:LS-1@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20251008T113000Z
DTEND:20251008T123000Z
SUMMARY:Dirac bundles and Dirac operators
DESCRIPTION:Speaker: Lukas Schönlinner\nWe will define Clifford algebras\, Clifford bundles and Dirac bundles. Every Dirac bundle carries an associated Dirac operator and we will prove the Weitzenböck formula in this general setup\, which is one of the most important tools in spin geometry.\n\nhttps://topogeoiiitd.github.io/series/spin-geometry-and-scalar-curvature-rigidity/#LS-1
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/spin-geometry-and-scalar-curvature-rigidity/#LS-1
END:VEVENT
BEGIN:VEVENT
UID:LS-2@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20251016T093000Z
DTEND:20251016T103000Z
SUMMARY:Spin manifolds
DESCRIPTION:Speaker: Lukas Schönlinner\nIn this talk\, we will introduce the spin groups and discuss the properties necessary to define spinable manifolds. We will then associate a canonical connection\, the so-called spin connection\, with every spin manifold $M$. This connection induces a Dirac bundle structure on $M$. The associated Dirac operator satisfies the Schrödinger-Lichnerowicz formula\,  a special case of the Weitzenböck formula. Additionally\, we will discuss the Atiyah-Singer index theorem\, which links the index of the Dirac operator to topological properties of the manifold. These equations are the key features of spin geometry that we will exploit later.\n\nhttps://topogeoiiitd.github.io/series/spin-geometry-and-scalar-curvature-rigidity/#LS-2
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/spin-geometry-and-scalar-curvature-rigidity/#LS-2
END:VEVENT
BEGIN:VEVENT
UID:LS-3@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20251022T113000Z
DTEND:20251022T123000Z
SUMMARY:Llarull's theorem and generalizations
DESCRIPTION:Speaker: Lukas Schönlinner\nThe theorem of Llarull is a famous rigidity result in scalar curvature which states the following: Let $(M\,g)$ be a closed connected $n$-dimensional smooth Riemannian spin manifold with $n\\geq2$ even and $\\mathrm{scal}_g \\geq n(n-1)$. If $f\\colon M\\to S^n$ is a smooth 1-Lipschitz map of non-zero degree then $f$ is a Riemannian isometry.\n\nWe will discuss a generalization of this theorem\, which states that it is sufficient to assume that $g$ is a metric of Sobolev regularity $W^{1\,p}$ with $p> n$ and that $f$ is merely 1-Lipschitz instead of smooth.\n\nThis is joint work with Simone Cecchini\, Bernhard Hanke\, and Thomas Schick.\n\nhttps://topogeoiiitd.github.io/series/spin-geometry-and-scalar-curvature-rigidity/#LS-3
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/spin-geometry-and-scalar-curvature-rigidity/#LS-3
END:VEVENT
BEGIN:VEVENT
UID:LS-4@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20251029T113000Z
DTEND:20251029T123000Z
SUMMARY:Scalar curvature rigidity for manifolds with cone singularities
DESCRIPTION:Speaker: Lukas Schönlinner\nIn this talk\, we will discuss another generalization of Llarull's theorem in even dimensions where we allow cone-like singularities in the domain. To do so\, we will discuss an abstract functional analytic setup that enables us to show that the Dirac operator on these singular spaces is Fredholm. Moreover\, we will apply an index formula of Chou together with a deformation argument to show that the index is non-zero.\n\nThis is joint work with Simone Cecchini\, Bernhard Hanke\, and Thomas Schick.\n\nhttps://topogeoiiitd.github.io/series/spin-geometry-and-scalar-curvature-rigidity/#LS-4
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/spin-geometry-and-scalar-curvature-rigidity/#LS-4
END:VEVENT
BEGIN:VEVENT
UID:SR-1@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20251105T113000Z
DTEND:20251105T123000Z
SUMMARY:Motivation. Groups as metric spaces
DESCRIPTION:Speaker: Sergio Romero Alba\nWe review\, through examples\, the foundational philosophy of Geometric Group Theory\, where each group $G$ with a finite generating set $S$ is associated with a metric space $(G\, dS)$\, translating algebraic properties of the group into geometric features of the space. Although this assignment initially depends on the choice of $S$\, such dependence vanishes when viewing $(G\, dS)$ "from infinitely far away". This motivates the introduction of coarse structures.\n\nhttps://topogeoiiitd.github.io/series/coarse-cohomology/#SR-1
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/coarse-cohomology/#SR-1
END:VEVENT
BEGIN:VEVENT
UID:SR-2@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20251112T113000Z
DTEND:20251112T123000Z
SUMMARY:Coarse cohomology and the coarse category. Basic properties
DESCRIPTION:Speaker: Sergio Romero Alba\nThe coarse cohomology $HX^*(X)$ of a space $X$ is introduced as a functor from the coarse category\, and its coarse invariance is discussed. We then particularize to metric spaces and study a few examples.\n\nhttps://topogeoiiitd.github.io/series/coarse-cohomology/#SR-2
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/coarse-cohomology/#SR-2
END:VEVENT
BEGIN:VEVENT
UID:SR-3@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20251119T113000Z
DTEND:20251119T123000Z
SUMMARY:Ideals of contractible DGAs. The Roe product in coarse cohomology
DESCRIPTION:Speaker: Sergio Romero Alba\nWe refine the structure of $HX^*(X)$\, enhancing it to an algebra by endowing it with a product. Much like the cup product [3\, §3.2] allows for a finer distinction between topological spaces\, it is natural to seek products in coarse cohomology that sharpen the information it provides. A first strategy is to adapt the cup product to this context\, but the resulting product in coarse cohomology turns out to be trivial. However\, not all is lost: in such cases\, one can define Massey triple products. In this session\, we will introduce a closely related idea: the Roe product in coarse cohomology [5\, §2.4]. This procedure can be abstracted to an algebraic setting\, whose potential will later be exploited again.\n\nhttps://topogeoiiitd.github.io/series/coarse-cohomology/#SR-3
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/coarse-cohomology/#SR-3
END:VEVENT
BEGIN:VEVENT
UID:SR-4@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20251126T113000Z
DTEND:20251126T123000Z
SUMMARY:Topological bornological spaces and their cohomology
DESCRIPTION:Speaker: Sergio Romero Alba\nThe category $\\mathrm{TopBorn}$ of topological bornological spaces is defined\, as in [2\, §7.1.1]. We propose an invariant $HB^*$ on these spaces\, which we call bornological cohomology\, and show that it can be determined from the Alexander-Spanier cohomology at infinity. We compute several examples and enrich $HB^*$ with a product\, endowing it with the structure of a differential graded algebra.\n\nhttps://topogeoiiitd.github.io/series/coarse-cohomology/#SR-4
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/coarse-cohomology/#SR-4
END:VEVENT
BEGIN:VEVENT
UID:SR-5@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20251203T100000Z
DTEND:20251203T110000Z
SUMMARY:Low degree cohomology\, extension spaces and boundaries at infinity. Open problems
DESCRIPTION:Speaker: Sergio Romero Alba\nIt is well known that the degree-zero singular homology of a topological space is determined by its path-connected components. Similarly\, degree-zero Alexander-Spanier cohomology can be computed from its connected components. We ask whether\, for a topological bornological space $X$\, there exists a similar connection between $HB^{1}(X)$ and the ``components at infinity of $X$''. \n\nThis question naturally leads us to give meaning to notions such as rays in $X$\, (path-)connected components at infinity\, and ultimately to consider compactifications of $X$. After addressing this question\, we generalize the tools involved by studying certain extensions of $X$ whose boundaries at infinity are Stone spaces [4]\, which can therefore be treated dually as topological spaces or as Boolean algebras (this is recent work in progress). \n\nWe will conclude the course by reviewing some questions that remain open.\n\nhttps://topogeoiiitd.github.io/series/coarse-cohomology/#SR-5
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/coarse-cohomology/#SR-5
END:VEVENT
BEGIN:VEVENT
UID:SS-1@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260120T103000Z
DTEND:20260120T113000Z
SUMMARY:Foundations and Basic Examples
DESCRIPTION:Speaker: Sandip Samanta\nWe provide an overview of the group of self-homotopy equivalences\, $\\mathcal{E}(X) = \\{[f] \\mid f: X \\simeq X\\}$\, focusing on key subgroups such as those acting trivially on homotopy or cohomology groups. We summarize the known structures of $\\mathcal{E}(X)$ for spaces like spheres and low-dimensional complexes. The discussion includes exact sequences relating $\\mathcal{E}(X)$ for products and wedge sums. Finally\, we explore various generalizations obtained by considering free-\, fiber-\, equivariant-\, and $H$-homotopy equivalences\, highlighting their algebraic and geometric significance through classical results.\n\nhttps://topogeoiiitd.github.io/series/on-the-groups-of-self-homotopy-equivalences/#SS-1
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/on-the-groups-of-self-homotopy-equivalences/#SS-1
END:VEVENT
BEGIN:VEVENT
UID:SS-2@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260127T123000Z
DTEND:20260127T133000Z
SUMMARY:Some Computations
DESCRIPTION:Speaker: Sandip Samanta\nWe survey explicit computations of the group of self-homotopy equivalences $\\mathcal{E}(X)$ for key spaces in homotopy theory. This includes results for pseudo-projective planes\, with emphasis on lens spaces\, as well as for Moore spaces $M(G\, n)$ and twisted Eilenberg-MacLane spaces. We also discuss the structure of $\\mathcal{E}(X)$ for real\, complex\, and quaternionic projective spaces. Additionally\, we present computations of $\\mathcal{E}_H(X)$ for rank one $H$-spaces\, specifically $S^1$\, $S^3$\, $S^7$\, $\\mathbb{R}P^3$\, $\\mathbb{R}P^7$\, and for certain higher-dimensional examples such as $S^3\\times S^7$\, $S^3\\times S^3$\, $S^7\\times S^7$\, $SU(3)$\, and $Sp(2)$. These cases illustrate the diversity and depth of self-equivalence groups across notable spaces in topology.\n\nhttps://topogeoiiitd.github.io/series/on-the-groups-of-self-homotopy-equivalences/#SS-2
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/on-the-groups-of-self-homotopy-equivalences/#SS-2
END:VEVENT
BEGIN:VEVENT
UID:SS-3@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260203T133000Z
DTEND:20260203T143000Z
SUMMARY:Algebraic Connection\, Localization and Open Problems
DESCRIPTION:Speaker: Sandip Samanta\nHere we will briefly see the ingredients of rational homotopy theory\, like rationalization of spaces\, Sullivan (minimal) models\, LS category\, etc\, and compute some basic examples. Finally\, we will relate these to our case of self-homotopy equivalences\, like how $\\mathcal{E}(X)$ and $\\mathcal{E}(X_\\mathcal{P})$ are related\, some other results and possible open directions.\n\nhttps://topogeoiiitd.github.io/series/on-the-groups-of-self-homotopy-equivalences/#SS-3
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/on-the-groups-of-self-homotopy-equivalences/#SS-3
END:VEVENT
BEGIN:VEVENT
UID:SK-1@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260210T103000Z
DTEND:20260210T113000Z
SUMMARY:Basic notions of knot theory
DESCRIPTION:Speaker: Seongjeong Kim\nWe introduce basic definitions and fundamental results in knot theory. One of the simplest knot invariants is the coloring invariant\, which can detect certain nontrivial knots. As a generalization of the coloring invariant\, we define an algebraic structure called a quandle.\n\nhttps://topogeoiiitd.github.io/series/knot-theory/#SK-1
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/knot-theory/#SK-1
END:VEVENT
BEGIN:VEVENT
UID:SK-2@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260217T103000Z
DTEND:20260217T113000Z
SUMMARY:Kauffman bracket and the colored Jones polynomial
DESCRIPTION:Speaker: Seongjeong Kim\nWe introduce the Kauffman bracket and the Jones polynomial\, which arise naturally in quantum topology and statistical mechanics. As an extension of the Jones polynomial\, we also introduce the colored Jones polynomial.\n\nhttps://topogeoiiitd.github.io/series/knot-theory/#SK-2
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/knot-theory/#SK-2
END:VEVENT
BEGIN:VEVENT
UID:SK-3@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260224T103000Z
DTEND:20260224T113000Z
SUMMARY:Knot theory and low-dimensional topology
DESCRIPTION:Speaker: Seongjeong Kim\nThe goal of this lecture is to explain how closed 3-manifolds can be constructed via surgery along framed links. We briefly review the notion of handle decompositions of manifolds and then describe how framed knots and links give rise to 3-manifolds.\n\nhttps://topogeoiiitd.github.io/series/knot-theory/#SK-3
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/knot-theory/#SK-3
END:VEVENT
BEGIN:VEVENT
UID:DM-1@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260310T103000Z
DTEND:20260310T113000Z
SUMMARY:Diffeology: definitions and examples
DESCRIPTION:Speaker: David Miyamoto\nWe will introduce the category of diffeological spaces\, and give several examples: the cusp \\(x^2 = y^3\\)\, as a subset of \\(\\mathbb{R}^2\\)\; the irrational tori \\(\\mathbb{R}/(\\mathbb{Z} + \\alpha\\mathbb{Z})\\)\, for irrational \\(\\alpha\\)\; and the diffeomorphism group of the real line\, \\(\\operatorname{Diff}(\\mathbb{R})\\). These will illustrate how the category of diffeological spaces is closed under taking\, respectively\, subsets\, quotients\, and mapping spaces\, and help give a sense of the data contained within a diffeological structure.\n\nhttps://topogeoiiitd.github.io/series/diffeology/#DM-1
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/diffeology/#DM-1
END:VEVENT
BEGIN:VEVENT
UID:DM-2@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260317T103000Z
DTEND:20260317T113000Z
SUMMARY:Higher and infinite-dimensional structures in geometry
DESCRIPTION:Speaker: David Miyamoto\nWe will introduce two other approaches to singular and infinite-dimensional spaces\, namely Lie groupoids (a step towards differentiable stacks)\, and convenient infinite-dimensional manifold structures. We will then explore how relevant diffeological spaces appear in both contexts.\n\nhttps://topogeoiiitd.github.io/series/diffeology/#DM-2
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/diffeology/#DM-2
END:VEVENT
BEGIN:VEVENT
UID:DM-3@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260324T103000Z
DTEND:20260324T113000Z
SUMMARY:Diffeological geometry
DESCRIPTION:Speaker: David Miyamoto\nHaving completed the introductions\, we will summarize some recent progress in using diffeology to understand geometry. Among these will include: a generalization of the Serre-Swan theorem using diffeological vector bundles\; an integration of Lie algebroids to diffeological groupoids\, even when no integrating Lie groupoid exists\; and a diffeological approach to the question of geometric quantization.\n\nhttps://topogeoiiitd.github.io/series/diffeology/#DM-3
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/diffeology/#DM-3
END:VEVENT
BEGIN:VEVENT
UID:AD-1@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260414T103000Z
DTEND:20260414T113000Z
SUMMARY:Introduction to minimal and maximal surfaces in $\\mathbb{R}^3$ and $\\mathbb{L}_1^3$ respectively
DESCRIPTION:Speaker: Anu Dhochak\nIn this talk\, we will discuss minimal and maximal surfaces in three-dimensional Euclidean and Lorentz-Minkowski space respectively. We will explore how they are related and how to construct them. In particular\, we will cover Björling problem and Weierstrass-Ennerper representations for them. I will also define the term maxface on which my next two lectures will be.\n\nhttps://topogeoiiitd.github.io/series/existence-of-arbitrary-genus-maxfaces-in-the-lorentz-minkowski-space/#AD-1
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/existence-of-arbitrary-genus-maxfaces-in-the-lorentz-minkowski-space/#AD-1
END:VEVENT
BEGIN:VEVENT
UID:AD-2@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260421T103000Z
DTEND:20260421T113000Z
SUMMARY:Node-opening construction of maxfaces
DESCRIPTION:Speaker: Anu Dhochak\nIn this talk\, we will discuss the existence of a 1-parameter family of arbitrary genus maxfaces with an arbitrary number of spacelike ends and infinitely many swallowtails. Our primary tool of construction will be node-opening technique. All maxfces of these families are embedded in a wider sense. We will also see families of Lorentzian Costa and Costa-Hoffman-Meeks surfaces\, as well as periodic surfaces of infinite genus\, as examples.\n\nhttps://topogeoiiitd.github.io/series/existence-of-arbitrary-genus-maxfaces-in-the-lorentz-minkowski-space/#AD-2
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/existence-of-arbitrary-genus-maxfaces-in-the-lorentz-minkowski-space/#AD-2
END:VEVENT
BEGIN:VEVENT
UID:RB-1@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260825T033000Z
DTEND:20260825T043000Z
SUMMARY:Non-Commutative Witt Vectors\, Characteristic Map and Pairing I
DESCRIPTION:Speaker: Ramyak Bilas\nFor a commutative ring \\(A\\)\, the ring of Witt vectors \\(W(A)\\) has been useful in number theory\, algebraic topology\, and algebraic K-theory. Classical results of Almkvist\, Stienstra\, Grayson\, and Weibel demonstrate that the characteristic map bridges the ring \\(\\operatorname{End}_0(R)\\) to its \\(t\\)-adic completion \\(W(A)\\)\, and the nil groups \\(\\operatorname{Nil}_0(A)\\) are modules over \\(W(A)\\). Recently Dotto\, Krause\, Nikolaus\, and Patchkoria (DKNP) gave an algebraic description of Witt vectors for a non-commutative ring \\(R\\). While attempting to generalize this framework to non-commutative rings \\(R\\) strips away significant algebraic structure\, \\(\\operatorname{End}_0(R)\\) is reduced to an abelian group with only an external product. Furthermore\, the foundational arguments about the interaction of Frobenius\, Verschiebung\, and the pairings rely on the Cayley-Hamilton theorem\, which breaks down in the non-commutative setting. This first talk will give an introduction to these new definitions of Witt vectors and the DKNP definition of the characteristic map.\n\nhttps://topogeoiiitd.github.io/series/non-commutative-witt-vectors-characteristic-map-and-pairing/#RB-1
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/non-commutative-witt-vectors-characteristic-map-and-pairing/#RB-1
END:VEVENT
BEGIN:VEVENT
UID:RB-2@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260827T033000Z
DTEND:20260827T043000Z
SUMMARY:Non-Commutative Witt Vectors\, Characteristic Map and Pairing II
DESCRIPTION:Speaker: Ramyak Bilas\nIf one takes the view of Witt vectors as the \\(t\\)-adic completion of \\(\\operatorname{End}_0(R)\\)\, then one can essentially circumvent the use of the trace property and the Witt vectors with coefficients used in DKNP\, and recover every property of the Witt vectors as a consequence of the K-theoretic properties of \\(\\operatorname{End}_0(R)\\). This second talk will focus on an alternate definition of Witt vectors and the characteristic map\, and additionally give an external pairing of Witt vectors and \\(\\operatorname{Nil}_0(R)\\).\n\nhttps://topogeoiiitd.github.io/series/non-commutative-witt-vectors-characteristic-map-and-pairing/#RB-2
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/non-commutative-witt-vectors-characteristic-map-and-pairing/#RB-2
END:VEVENT
BEGIN:VEVENT
UID:RL-1@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260903T083000Z
DTEND:20260903T093000Z
SUMMARY:Foliations and Singular Foliations
DESCRIPTION:Speaker: Ruben Louis\nWe will introduce the notions of regular and singular foliations\, discuss their main features\, and present some motivating examples.\n\nhttps://topogeoiiitd.github.io/series/ruben/#RL-1
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/ruben/#RL-1
END:VEVENT
BEGIN:VEVENT
UID:RL-2@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260910T083000Z
DTEND:20260910T093000Z
SUMMARY:Poisson Manifolds and Poisson \\(C^\\infty\\)-Rings
DESCRIPTION:Speaker: Ruben Louis\nWe will introduce the notion of \\(C^\\infty\\)-rings and study Poisson structures in this setting. We will then discuss their relationship with singular foliations and\, more generally\, with Lie-Rinehart algebras.\n\nhttps://topogeoiiitd.github.io/series/ruben/#RL-2
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/ruben/#RL-2
END:VEVENT
BEGIN:VEVENT
UID:RL-3@topogeoiiitd
DTSTAMP:20260912T000409Z
DTSTART:20260924T083000Z
DTEND:20260924T093000Z
SUMMARY:Lie-Rinehart and Poisson Algebras over \\(C^\\infty\\)-Rings
DESCRIPTION:Speaker: Ruben Louis\nWe will present a recent result extending the Courant correspondence to Lie–Rinehart algebras over \\(C^\\infty\\)-rings\, based on joint work with Eugene Lerman.\n\nhttps://topogeoiiitd.github.io/series/ruben/#RL-3
LOCATION:Online
URL:https://topogeoiiitd.github.io/series/ruben/#RL-3
END:VEVENT
END:VCALENDAR