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DTSTART:20250309T070000
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DTSTART:20241103T060000
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BEGIN:VEVENT
UID:6828a973281ff
DTSTART;TZID=America/Toronto:20250523T153000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20250523T163000
URL:/combinatorics-and-optimization/events/tutte-colloq
 uium-david-torregrossa-belen
SUMMARY:Tutte colloquium-David Torregrossa Belén
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE:Splitting algorithms for monotone inclusions 
 with\nminimal dimension\n\nSPEAKER:\n David Torregrossa Belén\n\nAFFILIA
 TION:\n Center for Mathematical Modeling\, University of Chile\n\nLOCATIO
 N:\n MC 5501\n\nABSTRACT: Many situations in convex optimization can be mo
 deled as the\nproblem of finding a zero of a monotone operator\, which ca
 n be\nregarded as a generalization of the gradient of a differentiable\nc
 onvex function. In order to numerically address this monotone\ninclusion 
 problem\, it is vital to be able to exploit the inherent\nstructure of th
 e operator defining it. The algorithms in the family\nof the splitting me
 thods achieve this by iteratively solving simpler\nsubtasks that are defi
 ned by separately using some parts of the\noriginal problem.\n\nIn the fi
 rst part of this talk\, we will introduce some of the\nmost relevant mono
 tone inclusion problems and present their\napplications to optimization. 
 Subsequently\, we will draw our\nattention to a common anomaly that has p
 ersisted in the design of\nmethods in this family: the dimension of the u
 nderlying space\n—which we denote as lifting— of the algorithms abnor
 mally\nincreases as the problem size grows. This has direct implications 
 on\nthe computational performance of the method as a result of the\nincre
 ase of memory requirements. In this framework\, we characterize\nthe mini
 mal lifting that can be obtained by splitting algorithms\nadept at solvin
 g certain general monotone inclusions. Moreover\, we\npresent splitting m
 ethods matching these lifting bounds\, and\nthus having minimal lifting.\
 n\n \n 
DTSTAMP:20250517T152123Z
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BEGIN:VEVENT
UID:6828a973294e5
DTSTART;TZID=America/Toronto:20250516T153000
SEQUENCE:0
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DTEND;TZID=America/Toronto:20250516T163000
URL:/combinatorics-and-optimization/events/tutte-colloq
 uium-michael-borinsky
SUMMARY:Tutte colloquium-Michael Borinsky
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE:Constraining moduli space cohomology by count
 ing graphs\n\nSPEAKER:\n Michael Borinsky\n\nAFFILIATION:\n Perimeter Inst
 itute\n\nLOCATION:\n MC 5501\n\nABSTRACT: In 1992\, Kontsevich defined com
 plexes spanned by graphs.\nThese \ncomplexes are increasingly prominent i
 n algebraic topology\,\ngeometric \ngroup theory and mathematical physics
 . For instance\, a 2021 theorem\nby \nChan-Galatius and Payne implies tha
 t the top-weight cohomology of\nthe \nmoduli space of curves of genus g i
 s equal to the homology of a\nspecific \ngraph complex. I will present a 
 new theorem on the asymptotic growth \nrate of the Euler characteristic o
 f this graph complex and explain\nits \nimplication on the cohomology of 
 the moduli space of curves. The\nproof \ninvolves solving a specific grap
 h counting problem.\n\n \n 
DTSTAMP:20250517T152123Z
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BEGIN:VEVENT
UID:6828a9732a05c
DTSTART;TZID=America/Toronto:20250512T113000
SEQUENCE:0
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DTEND;TZID=America/Toronto:20250512T123000
URL:/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-lorenzo-ciardo
SUMMARY:Algebraic Graph Theory-Lorenzo Ciardo
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE: Alice\, Bob\, and colours: An algebraic app
 roach to quantum\nadvantage\n\nSPEAKER:\n\nLorenzo Ciardo\n\nAFFILIATION:\
 n University of Oxford\n\nLOCATION:\n Please contact Sabrina Lato for Zo
 om link.\n\nABSTRACT: Two-player one-round games exhibit quantum advantag
 e if the\navailability of quantum resources results in non-classical\ncorr
 elations between the players' answers\, which allow outperforming\nany cla
 ssical strategy. The first part of the talk illustrates a link\nbetween (i
 ) the occurrence of quantum advantage in a game\, and (ii)\nthe complexity
  of the corresponding classical computational problem.\nIn particular\, I 
 will show that both (i) and (ii) are determined by\nthe same algebraic inv
 ariants of the game\, known as polymorphisms.\nThis allows transferring me
 thods from the universal-algebraic theory\nof constraint satisfaction to t
 he setting of quantum advantage. In\nparticular\, this approach yields a c
 omplete characterisation of the\noccurrence of quantum advantage for games
  played on graphs.   \n\nThe second part of the talk outlines recent wor
 k on the quantum\nchromatic number introduced in\n[Cameron--Montanaro--New
 man--Severini--Winter'07]. The gap between\nthis parameter and its classic
 al counterpart is a measure of quantum\nadvantage for the graph colouring 
 game. Using the polymorphic\napproach\, I will show that the maximum gap i
 s linear when the quantum\nchromatic number makes use of entangled strateg
 ies on a constant\nnumber of qubits. In contrast\, in the case of unlimite
 d entanglement\nresources\, I will prove the existence of graphs whose qua
 ntum\nchromatic number is 3 and whose classical chromatic number is\narbit
 rarily large\, conditional to the quantum variants of Khot's\nd-to-1 Conje
 cture [Khot'02] and HÃ¥stad's inapproximability of linear\nequations [HÃ¥s
 tad'01].\n 
DTSTAMP:20250517T152123Z
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DTSTART;TZID=America/Toronto:20250515T140000
SEQUENCE:0
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DTEND;TZID=America/Toronto:20250515T150000
URL:/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-felix
SUMMARY:Algebraic and enumerative combinatorics seminar-Félix Gelinas
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE:Source characterization of the hypegraphic po
 sets\n\nSpeaker\n Félix Gelinas\n\nAffiliation\n York\n\nLocation\n MC 5
 479\n\nABSTRACT: For a hypergraph $\\mathbb{H}$ on $[n]$\, the hypergraphi
 c\nposet $P_\\mathbb{H}$ is the transitive closure of the oriented\n$1$-sk
 eleton of the hypergraphic polytope $\\Delta_\\mathbb{H}$\, which\nis the 
 Minkowski sum of the standard simplices $\\Delta_H$ for each\nhyperedge $H
  \\in \\mathbb{H}$. In 2019\, C. Benedetti\, N. Bergeron\, and\nJ. Machace
 k established a remarkable correspondence between the\ntransitive closure 
 of the oriented $1$-skeleton of $\\Delta_\\mathbb{H}$\nand the flip graph 
 on acyclic orientations of $\\mathbb{H}$. Viewing an\norientation of $\\ma
 thbb{H}$ as a map $A$ from $\\mathbb{H}$ to $[n]$\,\nwe define the sources
  of the acyclic orientations as the values $A(H)$\nfor each hyperedge $H \
 \in \\mathbb{H}$. In a recent paper\, N. Bergeron\nand V. \n\nPilaud provi
 ded a characterization of $P_\\mathbb{H}$ based on the\nsources of acyclic
  orientations for interval hypergraphs.\nSpecifically\, two distinct acycl
 ic orientations $A$ and $B$ of\n$\\mathbb{H}$ are comparable in $P_\\mathb
 b{H}$ if and only if their\nsources satisfy $A(H) \\leq B(H)$ for all hype
 redges $H\\in \\HH$. The\ngoal of this work is to extend this source chara
 cterization of\n$P_\\mathbb{H}$ to arbitrary hypergraphs on $[n]$.\n\nTHER
 E WILL BE A PRE-SEMINAR PRESENTING RELEVANT BACKGROUND AT THE\nBEGINNING G
 RADUATE LEVEL STARTING AT 1:30PM\,\n 
DTSTAMP:20250517T152123Z
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DTSTART;TZID=America/Toronto:20250505T113000
SEQUENCE:0
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DTEND;TZID=America/Toronto:20250505T123000
URL:/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-venkata-raghu-tej-pantangi
SUMMARY:Algebraic Graph Theory-Venkata Raghu Tej Pantangi
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE: Random analogues of Erd\\H{o}s-Ko-Rado type
  results.\n\nSPEAKER:\n\nVenkata Raghu Tej Pantangi\n\nLOCATION:\n Please 
 contact Sabrina Lato for Zoom link.\n\nABSTRACT: The classical Erd\\H{o
 }s-Ko-Rado (EKR) theorem and its\nvariants can be translated into characte
 rizing maximum co-cliques of\ngraphs in Association schemes. For instance\
 , the classical\nErd\\H{o}s-Ko-Rado characterizes maximum co-cliques in th
 e Kneser\ngraph. Given a graph $G$\, by $G_{p}$\, we denote the random sub
 graph of\n$G$ in which edges appear independently\, each with a probabilit
 y $p$.\nIn this talk\, we consider the following question: for which\nprob
 abilities is the independence number of $G_{p}$ equal to that of\n$G$? Bol
 labas-Narayanan-Raigorodskii investigated the independence\nnumbers of ran
 dom subgraphs of the Kneser graph. In this talk\, we will\ninvestigate the
  independence numbers of random subgraphs of (i) the\nderangement graph on
  permutations\; and (ii) the perfect matching\ngraphs. The derangement gra
 ph is associated with the EKR type result\non permutations and the perfect
  matching graph is associated with EKR\ntype result on perfect matchings. 
 This is joint work with the members\nof the PIMS Collaborative Research Gr
 oup on Movement and Symmetry in\ngraphs.   \n 
DTSTAMP:20250517T152123Z
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BEGIN:VEVENT
UID:6828a9732bbfe
DTSTART;TZID=America/Toronto:20250509T153000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20250509T163000
URL:/combinatorics-and-optimization/events/tutte-colloq
 uium-luke-schaeffer
SUMMARY:Tutte colloquium-Luke Schaeffer
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE:Faster linear algebra using treewidth\n\nSPEA
 KER:\n Luke Schaeffer\n\nAFFILIATION:\n University of À¶Ý®ÊÓƵ\n\nLOCATION
 :\n MC 5501\n\nABSTRACT: \n\n: We look at the complexity of solving sparse
  linear systems as a\nfunction of the treewidth of the instance. That is\,
  the sparse matrix\nis associated with a sparse graph\, and solutions can 
 be found faster\nwhen that graph has low treewidth. We give a parameterize
 d algorithm\nin system size and treewidth achieving the conjectured optima
 l\nperformance.\n\nThis is joint work with Daniel Grier.\n\n \n 
DTSTAMP:20250517T152123Z
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DTSTART;TZID=America/Toronto:20250508T140000
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DTEND;TZID=America/Toronto:20250508T150000
URL:/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-maximilian
SUMMARY:Algebraic and enumerative combinatorics seminar-Maximilian Wiesmann
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE:Arrangements and Likelihood\n\nSpeaker\n Maxi
 milian Wiesmann\n\nAffiliation\n Max Planck\n\nLocation\n MC 5479\n\nABSTR
 ACT: In this talk\, we establish connections between hypersurface\narrange
 ments and likelihood geometry. The central object is the\nlikelihood corre
 spondence which captures the dependence between data\nand critical points 
 of the likelihood function of a statistical model\nparametrized by the pol
 ynomials defining the arrangement. In particle\nphysics\, this same object
  is known as the scattering correspondence.\nThe connection to hypersurfac
 e arrangements leads to a new description\nof the prime ideal of the likel
 ihood correspondence\, which is often\ncomputationally advantageous. This 
 description is based on the Rees\nalgebra of the likelihood module of the 
 arrangement\, a module closely\nrelated to the module of logarithmic deriv
 ations. We present results\nfor generic and graphic arrangements.\n\nTHERE
  WILL BE A PRE-SEMINAR PRESENTING RELEVANT BACKGROUND AT THE\nBEGINNING GR
 ADUATE LEVEL STARTING AT 1PM\,\n 
DTSTAMP:20250517T152123Z
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BEGIN:VEVENT
UID:6828a9732cec7
DTSTART;TZID=America/Toronto:20250605T140000
SEQUENCE:0
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DTEND;TZID=America/Toronto:20250605T150000
URL:/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-alex-fink
SUMMARY:Algebraic and enumerative combinatorics seminar-Alex Fink
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE:The external activity complex of a pair of ma
 troids\n\nSpeaker\n Alex Fink\n\nAffiliation\n Queen Mary University of Lo
 ndon \n\nLocation\n MC 5479\n\nABSTRACT: In 2016\, Ardila and Boocher were
  investigating the variety\nobtained by taking the closure of a linear spa
 ce within A^n in its\ncompactification (P^1)^n\; later work named this the
  \"matroid Schubert\nvariety\". Its Gröbner degenerations led them to def
 ine\, and study the\ncommutative algebra of\, the _external activity compl
 ex_ of a matroid.\nIf the matroid is on n elements\, this is a complex on 
 2n vertices\nwhose facets encode the external activity of bases.\n\nIn rec
 ent work with Andy Berget on Speyer's g-invariant\, we required a\ngeneral
 isation of the definition of external activity where the input\nwas a pair
  of matroids on the same ground set. We generalise many of\nthe results of
  Ardila--Boocher to this setting. Time permitting\, I'll\nalso present the
  tropical intersection theory machinery we use to\nunderstand the external
  activity complex of a pair.\n\nFor those who attended my talk at this yea
 r's CAAC on this paper\, the\ncontent of the present talk is meant to be c
 omplementary.\n\nTHERE WILL BE A PRE-SEMINAR PRESENTING RELEVANT BACKGROUN
 D AT THE\nBEGINNING GRADUATE LEVEL STARTING AT 1:30PM\,\n 
DTSTAMP:20250517T152123Z
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BEGIN:VEVENT
UID:6828a9732d865
DTSTART;TZID=America/Toronto:20250428T113000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20250428T123000
URL:/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-sidhanth-mohanty
SUMMARY:Algebraic Graph Theory-Sidhanth Mohanty
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE: Explicit Lossless Vertex Expanders\n\nSPEAK
 ER:\n\nSidhanth Mohanty\n\nAFFILIATION:\n\nMassachusetts Institute of Tech
 nology\n\nLOCATION:\n Please contact Sabrina Lato for Zoom link.\n\nABST
 RACT: We give the first construction of explicit constant-degree\nlossless
  vertex expanders. Specifically\, for any ε>0 and sufficiently\nlarge d\,
  we give an explicit construction of an infinite family of\nd-regular grap
 hs where every small set S of vertices has (1−ε)d|S|\nneighbors (which 
 implies (1−2ε)d|S| unique-neighbors). Our results\nalso extend naturall
 y to construct biregular bipartite graphs of any\nconstant imbalance\, whe
 re small sets on each side have strong\nexpansion guarantees. The graphs w
 e construct admit a free group\naction\, and hence realize new families of
  quantum LDPC codes of Lin\nand M. Hsieh with a linear time decoding algor
 ithm.\n\nOur construction is based on taking an appropriate product of a\n
 constant-sized lossless expander with a base graph constructed from\nRaman
 ujan Cayley cubical complexes.\n\nBased on joint work with Jun-Ting Hsieh\
 , Alexander Lubotzky\, Assaf\nReiner\, and Rachel Yun Zhang (https://arxiv
 .org/abs/2504.15087)\n 
DTSTAMP:20250517T152123Z
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BEGIN:VEVENT
UID:6828a9732e2ee
DTSTART;TZID=America/Toronto:20250425T153000
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DTEND;TZID=America/Toronto:20250425T163000
URL:/combinatorics-and-optimization/events/tutte-colloq
 uium-ahmad-abdi-2
SUMMARY:Tutte colloquium-Ahmad Abdi
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE:Strongly connected orientations and integer l
 attices\n\nSPEAKER:\n Ahmad Abdi\n\nAFFILIATION:\n London School of Econom
 ics and Political Science\n\nLOCATION:\n MC 5501\n\nABSTRACT: Let D = (V\,
  A) be a digraph whose underlying graph is\n2-edge-connected\, and let P b
 e the polytope whose vertices are the\nincidence vectors of arc sets whose
  reversal makes D strongly\nconnected. We study the lattice theoretic prop
 erties of the integer\npoints contained in a proper 'slanted' face F of P.
  We prove under a\nmild necessary condition that the 0\,1 points in F con
 tain\nan _integral_ _basis _B\, i.e.\, B is linearly independent\, and 
 every\nintegral vector in the linear of span of F is an integral linear\nc
 ombination of B. This result is surprising as the integer points in F\ndo 
 not necessarily form a _Hilbert basis_. \n\nOur result has consequences f
 or head-disjoint strong orientations in\nhypergraphs\, and also to a famou
 s conjecture by Woodall that the\nminimum size of a dicut of D\, say k\, i
 s equal to the maximum number of\ndisjoint dijoins. We prove a relaxation 
 of this conjecture\, by finding\nfor any odd prime number p\, a p-adic pac
 king of dijoins of value k and\nof support size at most 2|A|. We also prov
 e that the all-ones vector\nbelongs to the lattice generated by the 0\,1 p
 oints in F\, where F is\nthe face of P satisfying x(C) = 1 for every minim
 um dicut C.\n\nThis is based on joint work with Gerard Cornuejols\, Siyue 
 Liu\, and\nOlha Silina.\n\n \n\n \n 
DTSTAMP:20250517T152123Z
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