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TZOFFSETFROM:-0500
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DTSTART:19700308T020000
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DTSTART:19701101T020000
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BEGIN:VEVENT
UID:mathcal-8@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:GRAD CLUB (MATH'S GRADUATE FALL ORIENTATION LUNCH - Western)
DTSTART;TZID=America/Toronto:20260908T120000
DTEND;TZID=America/Toronto:20260908T130000
DESCRIPTION:
LOCATION:GRAD CLUB
END:VEVENT
BEGIN:VEVENT
UID:mathcal-10@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:Variation of Geometric Invariant Theory and Derived Categories for Toric Varieties. (Alex Zwart - Western)
DTSTART;TZID=America/Toronto:20260910T133000
DTEND;TZID=America/Toronto:20260910T143000
DESCRIPTION:A smooth projective toric variety $X$ corresponding to the fan $\\Sigma$ with rays $\\Sigma(1)$ induces an action of the Picard torus $G$ on the affine space $\\mathbb{A}^{\\Sigma(1)}$. A character $\\chi$ of $G$\, i.e. an element of $\\mathrm{Pic}(X)$\, determines a $G-$linearized line bundle $L_\\chi$ which can be used to form a GIT quotient. The characters that give non-trivial GIT quotients are precisely the ones that live in the effective cone in $\\mathrm{Pic}(X)_{\\mathbb{R}}$. We can set an equivalence relation on this cone by specifying characters to be equivalent if they give the same GIT quotient. This decomposes the effective cone into a fan where the relative interiors of the cones are the equivalence classes\, we call this fan the GIT fan and denote it by $\\Sigma_{GIT}(X)$ or $\\Sigma_{GIT}$ when $X$ is understood. A chamber is the relative interior of a maximal cone in this fan and a wall is the relative interior of a codimension 1 cone. Two chambers are adjacent if they share a wall and we study how the derived category is affected by ``crossing a wall".
     
     Specifically\, crossing a wall induces a semi-orthogonal decomposition for the toric variety corresponding to one of the chambers. We study this semi-orthogonal decomposition for the generalized del Pezzo varieties following [BDM20]. In [BDM20] they use this semi-orthogonal decomposition to show they have a full exceptional collection of line bundles for this class of varieties. At the end of this paper\, we present the beginning results towards a generalization of this work to the case of the Klyachko varieties of [VK85]. This work is motivated by [Pal25] where the author produces a strong $S_m\\times S_n$-stable\, but not full\, exceptional collection of line bundles for the Klyachko varieties in the case $n$ is congruent to 1 modulo $m$. 
 
LOCATION:MC 108
END:VEVENT
BEGIN:VEVENT
UID:mathcal-10@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:first Fall meeting ( - Western)
DTSTART;TZID=America/Toronto:20260910T153000
DTEND;TZID=America/Toronto:20260910T163000
DESCRIPTION:agenda by email!
LOCATION:MC 107
END:VEVENT
BEGIN:VEVENT
UID:mathcal-14@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA ( - Western)
DTSTART;TZID=America/Toronto:20260914T130000
DTEND;TZID=America/Toronto:20260914T140000
DESCRIPTION:
LOCATION:MC 204
END:VEVENT
BEGIN:VEVENT
UID:mathcal-14@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:The polytope of all matroids (Mieke Fink - Western)
DTSTART;TZID=America/Toronto:20260914T153000
DTEND;TZID=America/Toronto:20260914T163000
DESCRIPTION:In this talk\, I will introduce the valuative group of matroids\, which
 allows to represent any matroid on the groundset $n$ of rank $r$ as a
 point in $\\mathbb R ^{n \\choose r}$. Many well-known matroid invariants behave as linear functions on the underlying vectorspace. 
 Ferroni and A. Fink initiated the
 study of the convex hull of all such points corresponding to matroids\,
 which they call the 'polytope of all matroids'. One reason to study the polytope is  to understand extremal behavior of matroid invariants.
 I will explain the construction and present first results on their polyhedral structure\, assuming no prior knowledge on matroids. 
 <p>
 
LOCATION:MC 108
END:VEVENT
BEGIN:VEVENT
UID:mathcal-15@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:Galois Category: Galois theory of Topology and Normal Curves (Roger (Qinghan) Yang - Western)
DTSTART;TZID=America/Toronto:20260915T113000
DTEND;TZID=America/Toronto:20260915T123000
DESCRIPTION:The purpose of this report is to explain why several categories which at first do not look like classical Galois
 theory nevertheless carry the same kind of Galois structure. We first study finite sets and finite continuous
 G-sets\, focusing on the categorical properties which they have in common. For the field theory\, the extension
 theorem motivates the fibre functor
 A ??? Homk(A\, ks)\,
 and leads to the anti-equivalence between finite Etale k-algebras and finite continuous Gk-sets. These examples
 then motivate the formal definition of a Galois category. We also discuss finite topological coverings as a Galois
 category and the topological Galois correspondence.
 The main example from algebraic geometric is obtained from normal curves. After reviewing the commutative
 algebra needed for normalization\, ramification\, residue-field extensions\, and etaleness\, we fix a nonempty open
 subset U of an integral proper normal curve X with function field K. We construct the compositum KU of the
 finite separable extensions of K whose corresponding normalizations are etale over U\, and define
 ?1(U) := Gal(KU/K).
 Using the anti-equivalence between normal curves and their function fields\, together with the field-theoretic
 Galois correspondence\, we show that the category of finite covers of X which are etale over U is equivalent to
 the category of finite continuous ?1(U)-sets. This gives the curve category its Galois-category structure.
 Finally\, we study what a finite quotient q : ?1(U) ? G means geometrically. Its kernel determines a
 finite Galois extension of K\, a corresponding cover of X\, and a finite-level Galois subcategory equivalent to the
 category of finite G-sets. Finally\, it concludes with monodromy and the Kummer cover x ?? xn\, which gives a
 concrete realization of the cyclic quotient ˆ? Z/nˆ? Z ?= Z/nZ.
LOCATION:MC 108
END:VEVENT
BEGIN:VEVENT
UID:mathcal-17@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:Higher-Order Networks: Topology and Geometry (Sara Najem - American University of Beirut)
DTSTART;TZID=America/Toronto:20260917T153000
DTEND;TZID=America/Toronto:20260917T163000
DESCRIPTION:Networks describe dyadic interactions and discard higher-order ones in complex systems. I will trace a path from weighted networks and their statistical-physics measures and show their limitations\, leading to simplicial complexes built from triangles\, tetrahedra\, and higher simplices that pairwise edges cannot encode. Topological invariants such as the Betti numbers\, the Euler characteristic\, torsion\, and the Ihara–Zeta function are introduced. Connes' spectral triplet then supplies geometric measures\, a spectral distance\, spectral dimension\, and a discrete curvature\, that complement these topological invariants. I will carry this out by illustrating the framework on a dataset of musical compositions\, where chords (notes played simultaneously) form natural higher-order structures.
LOCATION:MC 108
END:VEVENT
BEGIN:VEVENT
UID:mathcal-18@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:Cohomological rigidity of  smooth compact toric varieties (Suyoung Choi - Ajou University)
DTSTART;TZID=America/Toronto:20260918T143000
DTEND;TZID=America/Toronto:20260918T153000
DESCRIPTION:Toric varieties are a useful class of spaces where topology\, geometry\, and combinatorics are closely connected. In this talk\, I will discuss how we can classify smooth toric varieties from a topological point of view. I will first explain some basic ideas of topological classification and the role of cohomology. I will then introduce the cohomological rigidity problem and discuss some results for (generalized) Bott manifolds. Finally\, I will briefly talk about recent results on the classification of smooth Fano toric varieties.
LOCATION:MC 108
END:VEVENT
BEGIN:VEVENT
UID:mathcal-21@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA ( - Western)
DTSTART;TZID=America/Toronto:20260921T130000
DTEND;TZID=America/Toronto:20260921T140000
DESCRIPTION:
LOCATION:MC 204
END:VEVENT
BEGIN:VEVENT
UID:mathcal-21@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:Cohomological aspects of power ideals (Colin Crowley - Western)
DTSTART;TZID=America/Toronto:20260921T153000
DTEND;TZID=America/Toronto:20260921T163000
DESCRIPTION:Perhaps the most important invariant of an arrangement of hyperplanes is the associated matroid. Many cohomological invariants of the arrangement turn out to depend only on the underlying matroid\, and there has been much recent activity in the field of combinatorial Hodge theory which generalizes deep theorems from arrangements to abstract matroids. In this talk\, I'll discuss a bridge between these ideas\, and an area of algebraic combinatorics called Zonotopal algebra. Via this connection\, we can use tools from combinatorial Hodge theory to recover known results about zonotopal algebras as well as prove new ones\, including a conjecture of Rhoades\, Tewari\, and Wilson. We also explore new classes of zonotopal algebras inspired by vanishing results in combinatorial Hodge theory\, and vice versa.
LOCATION:MC 108
END:VEVENT
BEGIN:VEVENT
UID:mathcal-23@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:Liouville Theory Correlators and Weil–Petersson Geometry of the Moduli Spaces of Hyperbolic Cone Surfaces (Behrad Taghavi - Western)
DTSTART;TZID=America/Toronto:20260923T123000
DTEND;TZID=America/Toronto:20260923T133000
DESCRIPTION:Two-dimensional conformal field theory has proven a powerful tool in both physics and mathematics\, and one of its most striking applications is to the geometry of surfaces. This is clearest in Liouville theory\, which can be regarded as a quantum theory of two-dimensional geometry. Semiclassically\, a correlator of heavy vertex operators in this theory is governed by the on-shell Liouville action of a hyperbolic metric with conical singularities at the insertion points. In this talk\, I will study this on-shell Liouville action as a natural object on a deformation space of hyperbolic conical metrics\, and discuss how it encodes the geometry of that space.
 For compact surfaces of genus g>1 and punctured spheres\, this link goes back to Zograf and Takhtajan\, who showed that the on-shell Liouville action generates the accessory parameters of the uniformization problem and is a Kähler potential for the Weil–Petersson metric\; Park\, Takhtajan and Teo later extended this to higher-genus punctured surfaces. I will focus on the extension to case of orbifold Riemann surfaces with genus g>1: after cancelling an anomaly introduced by regularization at the conical points\, the modified action becomes a global Kähler potential for the combination of Weil–Petersson and Takhtajan–Zograf metrics appearing in the local index theorem for orbifold Riemann surfaces. Time permitting\, I will discuss ongoing work which aims to use CFT methods to obtain an asymptotic expansion of the Weil–Petersson Kähler form for small cone angles\, recovering the structure of Mirzakhani's formula for the Weil–Petersson class (with boundary components of purely imaginary length).
 <p>
 Based on joint work with A. Naseh and K. Allameh\, Phys. Rev. D 110 (2024) 046018\, and work in progress with A. Naseh.
LOCATION:MC 108
END:VEVENT
BEGIN:VEVENT
UID:mathcal-24@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:AI in Mathematics discussion (AI in Mathematics discussion - Western)
DTSTART;TZID=America/Toronto:20260924T153000
DTEND;TZID=America/Toronto:20260924T163000
DESCRIPTION:The role of LLMs in various aspects of the profession is increasingly of interest.  All are welcome to this discussion group.
LOCATION:MC 108
END:VEVENT
BEGIN:VEVENT
UID:mathcal-28@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA ( - Western)
DTSTART;TZID=America/Toronto:20260928T130000
DTEND;TZID=America/Toronto:20260928T140000
DESCRIPTION:
LOCATION:MC 204
END:VEVENT
BEGIN:VEVENT
UID:mathcal-30@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:From Harmonic Analysis on Trees to  p-adic AdS/CFT,  Part 1 (Masoud Khalkhali - Western)
DTSTART;TZID=America/Toronto:20260930T123000
DTEND;TZID=America/Toronto:20260930T133000
DESCRIPTION:This lecture series approaches \\(p\\)-adic AdS/CFT through the geometry and harmonic analysis of trees. Our guiding theme is the analogy between hyperbolic spaces\, Riemann surfaces\, and their non-Archimedean counterparts. Beginning with homogeneous trees and Cartier’s approach to their harmonic analysis\, we will study the Bruhat–Tits tree \\(\\mathcal T_K\\) associated with \\(\\mathrm{PGL}_2(K)\\)\, where \\(K\\) is a non-Archimedean local field. Its boundary at infinity is canonically identified with \\(\\mathbb P^1(K)\\)\, and the action on the tree extends the Möbius action on this boundary. This provides a geometric starting point for comparing the Archimedean and non-Archimedean settings.
 The first part develops the basic dictionary: geodesics and horocycles\, adjacency and Laplace operators\, spherical functions\, and boundary integral representations. Particular emphasis will be placed on the relationship between spectral theory in the interior and function theory on the boundary. We will also examine Schottky uniformization in the classical and non-Archimedean settings\, relating Riemann surfaces and hyperbolic handlebodies to Mumford curves and the quotient graphs that encode their skeletal geometry. These comparisons will illustrate both the power and the limitations of the tree analogy.
LOCATION:MC 108
END:VEVENT
BEGIN:VEVENT
UID:mathcal-31@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA (Kumar Shukla - Western)
DTSTART;TZID=America/Toronto:20261001T143000
DTEND;TZID=America/Toronto:20261001T153000
DESCRIPTION:
LOCATION:MC 108
END:VEVENT
BEGIN:VEVENT
UID:mathcal-35@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA ( - Western)
DTSTART;TZID=America/Toronto:20261005T130000
DTEND;TZID=America/Toronto:20261005T140000
DESCRIPTION:
LOCATION:MC 204
END:VEVENT
BEGIN:VEVENT
UID:mathcal-35@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA (Yu Li - Notre Dame University)
DTSTART;TZID=America/Toronto:20261005T153000
DTEND;TZID=America/Toronto:20261005T163000
DESCRIPTION:
LOCATION:MC 108
END:VEVENT
BEGIN:VEVENT
UID:mathcal-42@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA ( - Western)
DTSTART;TZID=America/Toronto:20261012T130000
DTEND;TZID=America/Toronto:20261012T140000
DESCRIPTION:
LOCATION:MC 204
END:VEVENT
BEGIN:VEVENT
UID:mathcal-49@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA ( - Western)
DTSTART;TZID=America/Toronto:20261019T130000
DTEND;TZID=America/Toronto:20261019T140000
DESCRIPTION:
LOCATION:MC 204
END:VEVENT
BEGIN:VEVENT
UID:mathcal-52@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA (Omid Amini - Ecole Polytechnique,  Paris)
DTSTART;TZID=America/Toronto:20261022T153000
DTEND;TZID=America/Toronto:20261022T163000
DESCRIPTION:
LOCATION:MC 108
END:VEVENT
BEGIN:VEVENT
UID:mathcal-56@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA ( - Western)
DTSTART;TZID=America/Toronto:20261026T130000
DTEND;TZID=America/Toronto:20261026T140000
DESCRIPTION:
LOCATION:MC 204
END:VEVENT
BEGIN:VEVENT
UID:mathcal-59@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA (Benjamin  Landon  - University of Toronto)
DTSTART;TZID=America/Toronto:20261029T153000
DTEND;TZID=America/Toronto:20261029T163000
DESCRIPTION:
LOCATION:MC 108
END:VEVENT
BEGIN:VEVENT
UID:mathcal-63@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA ( - Western)
DTSTART;TZID=America/Toronto:20261102T130000
DTEND;TZID=America/Toronto:20261102T140000
DESCRIPTION:
LOCATION:MC 204
END:VEVENT
BEGIN:VEVENT
UID:mathcal-70@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA ( - Western)
DTSTART;TZID=America/Toronto:20261109T130000
DTEND;TZID=America/Toronto:20261109T140000
DESCRIPTION:
LOCATION:MC 204
END:VEVENT
BEGIN:VEVENT
UID:mathcal-77@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA ( - Western)
DTSTART;TZID=America/Toronto:20261116T130000
DTEND;TZID=America/Toronto:20261116T140000
DESCRIPTION:
LOCATION:MC 204
END:VEVENT
BEGIN:VEVENT
UID:mathcal-84@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:TBA ( - Western)
DTSTART;TZID=America/Toronto:20261123T130000
DTEND;TZID=America/Toronto:20261123T140000
DESCRIPTION:
LOCATION:MC 204
END:VEVENT
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