BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Drupal iCal API//EN X-WR-CALNAME:Events items teaser X-WR-TIMEZONE:America/Toronto BEGIN:VTIMEZONE TZID:America/Toronto X-LIC-LOCATION:America/Toronto BEGIN:DAYLIGHT TZNAME:EDT TZOFFSETFROM:-0500 TZOFFSETTO:-0400 DTSTART:20260308T070000 END:DAYLIGHT BEGIN:STANDARD TZNAME:EST TZOFFSETFROM:-0400 TZOFFSETTO:-0500 DTSTART:20251102T060000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:6a6ecf14c2668 DTSTART;TZID=America/Toronto:20260807T153000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20260807T163000 URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq uium-michael-friedlander SUMMARY:Tutte Colloquium -Michael Friedlander- CLASS:PUBLIC DESCRIPTION:SPEAKER:\n Michael Friedlander\n\nAFFILIATION:\n University of British Columbia.\n\nLOCATION:\n MC 5501\n\nABSTRACT: TBA DTSTAMP:20260802T050108Z END:VEVENT BEGIN:VEVENT UID:6a6ecf14c6719 DTSTART;TZID=America/Toronto:20260810T140000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20260810T150000 URL:https://uwaterloo.ca/combinatorics-and-optimization/events/masters-thes is-presentation-david-evangelista-backedge SUMMARY:Master's Thesis Presentation - David Evangelista - Backedge Graphs of\nTournaments: Algorithms and Complexity CLASS:PUBLIC DESCRIPTION:SPEAKER:\n David Evangelista\n\nSUPERVISOR(S):\n Joseph Cheriya n and Sophie Spirkl\n\nCOMMITTEE:\n Jane Gao\, Eric Blais\n\nLOCATION:\n M C 5417\n\nABSTRACT: \n\nA tournament $\\T=(V\,A)$ on $n$ vertices is an o rientation of the\ncomplete graph $K_n$. The backedge graph of $T$ with re spect to an\nordering of $V$ is the undirected graph on vertex set $V$ who se edge\nset corresponds to the arcs directed from a later vertex to an ea rlier\nvertex in the ordering. Backedge graphs provide concise\nrepresenta tions of the tournament. The algorithmic problem of\ndetermining whether a tournament admits a backedge graph in a given\nclass of undirected graphs varies in complexity\, and is often\nequivalent to computing parameters o f tournaments\, such as\ndegreewidth when the backedge graph has bounded maximum degree\n\\cite{Davot et al.\, 2023}. We extend the notion of degre ewidth by\nintroducing directional degreewidth\, which separately bounds t he\nleft-degrees and right-degrees of vertices in addition to bounding the \ntotal degrees. We obtain an algorithm for verifying bounds on the\ndirec tional degreewidth of the tournament\, whose runtime is polynomial\ntime w hen the total degree is unbounded\, or fixed-parameter tractable\ntime wit h respect to the total degree bound otherwise. We also provide\na polynomi al-time algorithm for computing a $P_3$-free backedge graph\nof a tourname nt\, if it exists. Together with existing results\, the\nlatter result set tles the complexity of determining whether a\ntournament admits an $H$-fre e backedge graph when $H$ is any graph on\nthree vertices. DTSTAMP:20260802T050108Z END:VEVENT BEGIN:VEVENT UID:6a6ecf14c78c7 DTSTART;TZID=America/Toronto:20260806T130000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20260806T160000 URL:https://uwaterloo.ca/combinatorics-and-optimization/events/phd-defense- leo-jung-preprocessing-hard-optimization SUMMARY:PhD Defense - Leo Jung - Preprocessing for Hard Optimization Proble ms\nAcross Structurally Diverse Models CLASS:PUBLIC DESCRIPTION:SPEAKER:\n\nLeo Jung\n\nLOCATION:\n MC 5029\n\nABSTRACT: \n\nD ifficulties in solving large-scale optimization problems often arise\nfrom structural pathologies such as ill-conditioning\, Hadamard\nill-posedness \, and degeneracy\, particularly due to the failure of\nconstraint qualifi cations. While standard algorithms often struggle to\naddress these issues \, preprocessing based on structural analysis\noffers an effective strateg y for overcoming such challenges. This\nthesis investigates several prepro cessing methods targeting various\nsources of these difficulties. \nIn Par t I\, we study a nonclassical\, average condition number of linear\nsystem s\, the $\\omega$-condition number. Our results demonstrate\nseveral advan tages of the $\\omega$-condition number over the classical\n$\\kappa$-cond ition number. First\, $\\omega$ provides a more accurate\nmeasure of the c onditioning of linear systems by more faithfully\ncapturing the effects of perturbations observed in practice. Second\,\n$\\omega$ exhibits superior numerical stability compared to $\\kappa$.\nThird\, when used in precondi tioner design\, $\\omega$ more effectively\npromotes eigenvalue clustering \, which is crucial for the efficiency of\niterative solvers. Finally\, th e analytical simplicity of $\\omega$\nenables the derivation of explicit o ptimality conditions\, allowing for\nclosed-form expressions of optimal pr econditioners under various\nframeworks\, including low rank updates of th e generalized Jacobian for\nsemismooth Newton methods and diagonal or bloc k-diagonal scaling. For\ndiagonal preconditioning\, we further include a c omparison between two\ndistinct notions of conditioning. \nIn Part II\, we first answer in the affirmative a long-standing open\nquestion of whether the smooth stress function admits local nonglobal\nminimizers. This quart ic nonconvex objective function arises in the\nexact recovery of a Euclide an distance matrix (EDM) of a given\nembedding dimension. By eliminating t he Hadamard ill-posedness caused\nby translation and rotation invariance\, we stabilize Newton's method\nand avoid singular Hessians. \\\\ \nWe then consider the single-element error correction problem as a case\nstudy. We first show that the standard nearest EDM formulation based\non minimizing the smooth stress function fails to recover the correct\nEDM in this sett ing. We then introduce divide-and-conquer strategies\nbased on facial redu ction. Our approach efficiently recovers the\ncorrect EDM with high accura cy\, and we further provide criteria\ncharacterizing the existence of mult iple solutions. \nIn Part III\, we relate FR to the analysis of the conver gence behaviour\nof a semismooth Newton method for projection onto a spect rahedron\,\ni.e.\, the intersection of a linear manifold and the semidefin ite cone.\nIn this process\, we derive an explicit formula for the project ion onto\na face of the semidefinite cone obtained via regularization and\ nanalyze pathologies that arise in the absence of strict feasibility.\nWe further show that ill-conditioning of the Jacobian near optimality\ncharac terizes the degeneracy of the projection point. \\\\ \nAs an application\, we consider a simplified Wasserstein barycenter\nproblem\, a well-known N P-hard problem. We compute the Wasserstein\nbarycenter by exploiting the s tructure of the linear constraints to\nobtain a facially reduced doubly no nnegative (DNN) relaxation. This\nreduction provides a natural splitting f or applying the symmetric\nalternating direction method of multipliers (sA DMM). The resulting\nalgorithm exploits structure in the subproblems to co mpute strong\nupper and lower bounds. In most of the instances\, we achiev e the small\ngap between these bounds\, which means that the original prob lem is\nsolved. DTSTAMP:20260802T050108Z END:VEVENT BEGIN:VEVENT UID:6a6ecf14c87e3 DTSTART;TZID=America/Toronto:20260807T113000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20260807T123000 URL:https://uwaterloo.ca/combinatorics-and-optimization/events/combopt-read inggroup-david-aleman-unsplittable-0 SUMMARY:CombOpt ReadingGroup - David Aleman-Unsplittable multicommodity flo ws\nin fully planar instances CLASS:PUBLIC DESCRIPTION:SPEAKER:\n\n David Aleman\n\nAFFILIATION:\n University of Water loo\n\nLOCATION:\n MC 6029\n\nABSTRACT: \n\nThe multicommodity flow probl em involves routing multiple distinct\ncommodities through a shared networ k. An instance is given by\nan _undirected _graph G=(V\, E(G) ) with ed ge capacities\, and a\ncollection of source-sink pairs (s_i\,t_i) in V wit h associated\nnonnegative demands d(s_i\, t_i). It will be convenient to t hink of the\nsource-sink pairs as forming the edges of a demand graph H=( V\, E(H)\n). A flow is _feasible_ if it routes all demands without excee ding\nthe edge capacities\, and it is _unsplittable_ if it routes each\n demand along a single path. Let C be the smallest value such that the\nexi stence of a feasible flow implies the existence of an unsplittable\nflow t hat exceeds the edge capacities by at most an additivie amount\nof C times the maximum demand value.  \nWe show that if G+H = (V\, E(G) U E(H) ) is planar\, then  1.5<= C <=\n2. \nJoint work with Kumar\, Poremba\, and Sh epherd.    DTSTAMP:20260802T050108Z END:VEVENT BEGIN:VEVENT UID:6a6ecf14c9804 DTSTART;TZID=America/Toronto:20260731T113000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20260731T123000 URL:https://uwaterloo.ca/combinatorics-and-optimization/events/combopt-read inggroup-sina-kalantarzadeh-minimum-bounded SUMMARY:CombOpt ReadingGroup - Sina Kalantarzadeh-Minimum Bounded Degree\nS panning Trees CLASS:PUBLIC DESCRIPTION:SPEAKER:\n\n Sina Kalantarzadeh\n\nAFFILIATION:\n University of Waterloo\n\nLOCATION:\n MC 6029\n\nABSTRACT: I will present Goemans’s beautiful\, though no longer\nstate-of-the-art\, 2006 result on the Minimu m Bounded-Degree Spanning\nTree problem. Given a weighted graph (G=(V\,E)) and degree bounds\n(B\\to\\mathbb{N})\, the goal is to find a minimum-cos t spanning tree (T)\nsatisfying (d_T(v)\\le B(v)) for every (v\\in V). Thi s problem is\nNP-hard. Fürer and Raghavachari (1992) gave a polynomial-ti me\nalgorithm for the unweighted setting that produces a spanning tree\nsa tisfying (d_T(v)\\le B(v)+1). For the weighted problem\, Goemans\ndesigned an elegant LP-rounding algorithm that returns a tree of cost\nat most tha t of the optimal degree-bounded solution while satisfying\n(d_T(v)\\le B(v )+2). I will explain this result and the simple yet\nbeautiful combinatori al optimization ideas underlying it. In 2007\,\nSingh and Lau improved the violation to (B(v)+1) using iterative\nrelaxation\, which I might give a talk about in later sessions. DTSTAMP:20260802T050108Z END:VEVENT BEGIN:VEVENT UID:6a6ecf14ca4fc DTSTART;TZID=America/Toronto:20260805T140000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20260805T150000 URL:https://uwaterloo.ca/combinatorics-and-optimization/events/masters-thes is-presentation-martin-liu SUMMARY:Master's Thesis Presentation - Martin Liu CLASS:PUBLIC DESCRIPTION:SPEAKER:\n Martin Li\n\nSUPERVISOR(S):\n Vijay Bhattiprolu\n\nC OMITTEE:\n Jonathan Leake\, Levent Tuncel\n\nLOCATION:\n MC 6483\n\nABSTRA CT:\n\nThe $d$-dimensional Grothendieck constant is the smallest constant $K$\nsuch that \\begin{align*} \\sup\\left\\{\\sum_{i\,j=1}^n A_{ij}\\lang le\nu_i\,v_j\\rangle:u_i\,v_j\\in S^{d-1}\\right\\}\\le\nK\\cdot\\sup\\lef t\\{\\sum_{i\,j=1}^n\nA_{ij}x_iy_j:x_i\,y_j\\in\\{-1\,1\\}\\right\\} \\en d{align*}for any\n$n\\in\\mathbb{N}$ and any real $n\\times n$ matrix $A$. The inequality\nabove\, called the Grothendieck inequality\, has made a d eep impact in a\nvariety of areas such as functional analysis\, quantum in formation\ntheory\, and optimization. Determining the $d$-dimensional Grot hendieck\nconstant for any $d\\ge 3$ is a long-standing open problem.\n\nI n this paper\, we propose a worst operator in dimension 3\, whose\n$\\inft y\\to 1$ norm is conjectured to be $1/K_G(3)$. We study a related\nclass o f operators with nice geometric interpretations\, and we prove\nthe functi on $f:S^{d-1}\\to\\{-1\,1\\}$ corresponding to a hyperplane is\nuniquely o ptimal for this class\, with the isoperimetric inequality\nlying at the he art of our proof. DTSTAMP:20260802T050108Z END:VEVENT BEGIN:VEVENT UID:6a6ecf14cb1ef DTSTART;TZID=America/Toronto:20260804T120000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20260804T123000 URL:https://uwaterloo.ca/combinatorics-and-optimization/events/optimization -seminar-david-torregrosa-belen-convergence SUMMARY:Optimization seminar-David Torregrosa Belén-Convergence of a proxi mal\nstochastic subgradient method under the Kurdyka-Lojasiewicz condition CLASS:PUBLIC DESCRIPTION:SPEAKER:\n David Torregrosa Belén\n\nAFFILIATION:\n University of Alicante\n\nLOCATION:\n MC 5501\n\nABSTRACT:This talk presents a proxi mal stochastic subgradient\nmethod for minimizing the sum of an expected cost and a lower\nsemicontinuous\, prox-bounded function. We target a bro ad class of\nnonconvex integrands obeying a nonsmooth\, localized variant of the\ndescent lemma in the decision variable\, which in particular cov ers\nsmooth losses with Lipschitz gradient. At each iteration\, the\nexpe cted cost is replaced by a sample average that is progressively\nrefined\ , and the proximal stepsize is selected by an Armijo-type line\nsearch en forcing a\nsufficient decrease property up to stochastic errors induced by \nthe sample-based approximation. This framework accommodates more\ngener al problem formulations than existing methods and our analysis\nyields c onvergence guarantees that\, to the best of our knowledge\,\nare new even  in the smooth setting. Specifically\, we establish almost\nsure converg ence of the sequence of function values and stationarity\nof every accumu lation point of the trajectories under the relaxed\nrequirement that the sample-size sequence be merely nondecreasing and\nunbounded. Leveraging t he Kurdyka-Lojasiewicz property\, we further\nproof convergence of the wh ole trajectory to a single stationary\npoint. Finally\, for exponential-t ype desingularizing functions and\npolynomially growing sample sizes\, we derive explicit polynomial\nconvergence rates\, up to logarithmic factor \, for both the function\nvalues and the iterates. This is a joint work w ith Felipe Atenas\,\nPedro Pérez-Aros and Alejandro\nJofré\, from the Un iversity of Chile. DTSTAMP:20260802T050108Z END:VEVENT BEGIN:VEVENT UID:6a6ecf14cc2a3 DTSTART;TZID=America/Toronto:20260804T113000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20260804T120000 URL:https://uwaterloo.ca/combinatorics-and-optimization/events/optimization -seminar-ting-kei-pong-conditional-gradient SUMMARY:Optimization seminar-Ting Kei Pong-A Conditional-Gradient-Based\nSi ngle-Loop Augmented Lagrangian Method for Inequality Constrained\nProblems CLASS:PUBLIC DESCRIPTION:SPEAKER:\n Ting Kei Pong\n\nAFFILIATION:\n The Hong Kong Polyte chnic University\n\nLOCATION:\n MC 5501\n\nABSTRACT:We consider the proble m of minimizing the sum of a Lipschitz\ndifferentiable convex function an d a proper closed convex function\nthat admits efficient linear minimiza tion oracles\, subject to\nmultiple smooth convex inequality constraint s. We adapt the\nclassical augmented Lagrangian (AL) method for these pr oblems: in\neach iteration\, our algorithm consists of one step of condit ional\ngradient (CG) method applied to the AL function\, followed by\nan  update of the dual variable as in classical AL methods with a\ndiminish ing dual stepsize. We study the convergence rate of our\nalgorithm under two standard stepsize rules for the CG method\,\nnamely\, an open-loop s tepsize and the short stepsize\, and obtain a\nrate that matches the bes t-known complexity for this class of\nproblems. We also establish accele rated rates when\nthe aforementioned proper closed convex function is the  indicator\nfunction of a uniformly convex set. This is a joint work wit h\nXiaozhou Wang and Zev Woodstock. DTSTAMP:20260802T050108Z END:VEVENT BEGIN:VEVENT UID:6a6ecf14cd0af DTSTART;TZID=America/Toronto:20260730T143000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20260730T153000 URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an d-enumerative-combinatorics-seminar-maryam-yekta SUMMARY:Algebraic and Enumerative combinatorics seminar -Maryam Yekta-New\n bounds for integer flows and Verma modules via denormalized Lorentzian\nLa urent series CLASS:PUBLIC DESCRIPTION:SPEAKER:\n Maryam Yekta\n\nAFFILIATION:\n University of Waterlo o\n\nLOCATION:\n MC 5479\n\nABSTRACT: The theory of log concave polynomia ls has recently been\ndeveloped to study objects and problems in combinato rics and other\nsubfields in mathematics. Particular classes of log concav e\npolynomials called Lorentzian polynomials and denormalized and dually\n Lorentzian polynomials have been used to prove log concavity\nstatements f or various combinatorial sequences. This includes the\nstrongest form of M ason's log concavity conjecture on the independent\nsets of matroids and t he log concavity of sequences of Kostka numbers.\nIn this talk\, we develo p an analogous class of power series called\ndenormalized Lorentzian (DL) Laurent series. This class is the natural\ngeneralization of DL polynomial s to homogeneous power series with the\nbenefit of capturing a number of c ombinatorial generating series\nincluding the Kostant partition function f or integer flows of directed\ngraphs. We then analyze specific DL Laurent series to obtain new\nbounds for integral flows on general directed acycli c graphs and new\nbounds for the dimensions of weight spaces of parabolic\ n𝔰𝔩ₙ₊₁(ℂ) Verma modules.\n\nTHERE WILL BE A PRE-SEMINAR PRES ENTING RELEVANT BACKGROUND AT\nBEGINNING GRADUATE LEVEL STARTING AT 1:30PM IN MC 5417. DTSTAMP:20260802T050108Z END:VEVENT BEGIN:VEVENT UID:6a6ecf14cdf2f DTSTART;TZID=America/Toronto:20260731T153000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20260731T163000 URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq uium-kanstantsin-pashkovich-simple-and-almost SUMMARY:Tutte Colloquium -Kanstantsin Pashkovich-Simple and Almost\nNon-Ada ptive 1/2-Approximation for Matroid Prophet Inequalities CLASS:PUBLIC DESCRIPTION:SPEAKER:\n Kanstantsin Pashkovich\n\nAFFILIATION:\n University of Waterloo\n\nLOCATION:\n MC 5501\n\nABSTRACT: Prophet inequalities are a fundamental model for online\ndecision-making under uncertainty. For mat roid constraints\, Kleinberg\nand Weinberg gave a tight 1/2-approximation\ , but their algorithm uses\nadaptive thresholds that depend on the previou sly accepted elements.\nSpecifically\, the mechanism of Kleinberg and Wein berg accepts an\narriving element if and only if it is feasible to add wit h respect to\nthe matroid constraint and the value of the arriving element passes\nits threshold\; but this threshold depends on the elements accept ed so\nfar and on the arriving element itself. Later\, Feldman\, Svensson\ , and\nZenklusen showed that one can give a 1/4-approximation for general\ nmatroids. Their algorithm is almost non-adaptive\, i.e.\, it uses\nnon-ad aptive thresholds but changes the underlying matroid to another\n``stricte r'' matroid. Feldman\, Svensson\, and Zenklusen also showed\nthat no const ant approximation is possible in general matroids using\nnon-adaptive thre sholds if one does not change the underlying matroid.\n\nWe give a new alm ost non-adaptive algorithm for matroid prophet\ninequalities that achieves a 1/2 guarantee. We change the underlying\nmatroid to a ``stricter'' new matroid that is a direct sum of several\nmatroids. For each part of the ne w matroid\, we precompute a single\nnon-adaptive threshold. Once the eleme nts start to arrive\, we accept\nan arriving element as long as it is feas ible with respect to the new\n``stricter'' matroid and its value passes th e precomputed threshold.\nIn addition\, we guarantee that our algorithm ac hieves the 1/2\nguarantee not simply with respect to the prophet's expecte d gain\, but\nwith respect to the stronger ex-ante relaxation value. \nThu s\, we provide the first almost non-adaptive algorithm for the\nmatroid pr ophet inequality that achieves the best-possible\napproximation guarantee of 1/2. If time permits\, we will also discuss\nhow we used LLM in this pr oject. DTSTAMP:20260802T050108Z END:VEVENT END:VCALENDAR