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Average case polyhedral complexity of the maximum stable set problemNov 15 2013Mar 02 2016We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend on the input ... More

Bounds on the number of 2-level polytopes, cones and configurationsJun 15 2018We prove an upper bound of the form $2^{O(d^2 \mathrm{polylog}\,d)}$ on the number of affine (resp. linear) equivalence classes of, by increasing order of generality, 2-level d-polytopes, d-cones and d-configurations. This in particular answers positively ... More

The Virtual Private Network Design Problem with Concave Costs (Oberwolfach abstract)Dec 12 2008The symmetric Virtual Private Network Design (VPND) problem is concerned with buying capacity on links (edges) in a communication network such that certain traffic demands can be met. We investigate a natural generalization of VPND where the cost per ... More

On a Theorem of Sewell and TrotterDec 23 2007Feb 20 2008Sewell and Trotter [J. Combin. Theory Ser. B, 1993] proved that every connected alpha-critical graph that is not isomorphic to K_1, K_2 or an odd cycle contains a totally odd K_4-subdivision. Their theorem implies an interesting min-max relation for stable ... More

Poset Entropy versus Number of Linear Extensions: the Width-$2$ CaseFeb 20 2014Dec 03 2014Kahn and Kim (J. Comput. Sci., 1995) have shown that for a finite poset $P$, the entropy of the incomparability graph of $P$ (normalized by multiplying by the order of $P$) and the base-$2$ logarithm of the number of linear extensions of $P$ are within ... More

Approximating the Balanced Minimum Evolution ProblemApr 06 2011We prove a strong inapproximability result for the Balanced Minimum Evolution Problem. Our proof also implies that the problem remains NP-hard even when restricted to metric instances. Furthermore, we give a MST-based 2-approximation algorithm for the ... More

A tighter Erdös-Pósa function for long cyclesMay 04 2012We prove that there exists a bivariate function f with f(k,l) = O(l k log k) such that for every naturals k and l, every graph G has at least k vertex-disjoint cycles of length at least l or a set of at most f(k,l) vertices that meets all cycles of length ... More

Uncapacitated Flow-based Extended FormulationsJun 13 2013An extended formulation of a polytope is a linear description of this polytope using extra variables besides the variables in which the polytope is defined. The interest of extended formulations is due to the fact that many interesting polytopes have ... More

Improved approximation algorithms for hitting 3-vertex pathsAug 30 2018We study the problem of deleting a minimum cost set of vertices from a given vertex-weighted graph in such a way that the resulting graph has no induced path on three vertices. This problem is often called cluster vertex deletion in the literature and ... More

Hitting Diamonds and Growing CactiNov 23 2009Mar 21 2010We consider the following NP-hard problem: in a weighted graph, find a minimum cost set of vertices whose removal leaves a graph in which no two cycles share an edge. We obtain a constant-factor approximation algorithm, based on the primal-dual method. ... More

Cut dominants and forbidden minorsFeb 26 2015The cut dominant of a graph is the unbounded polyhedron whose points are all those that dominate some convex combination of proper cuts. Minimizing a nonnegative linear function over the cut dominant is equivalent to finding a minimum weight cut in the ... More

Excluded Forest Minors and the Erdős-Pósa PropertyApr 23 2012May 23 2013A classical result of Robertson and Seymour states that the set of graphs containing a fixed planar graph $H$ as a minor has the so-called Erd\H{o}s-P\'osa property; namely, there exists a function $f$ depending only on $H$ such that, for every graph ... More

Improved approximation algorithms for hitting 3-vertex pathsAug 30 2018Feb 22 2019We study the problem of deleting a minimum cost set of vertices from a given vertex-weighted graph in such a way that the resulting graph has no induced path on three vertices. This problem is often called cluster vertex deletion in the literature and ... More

A closest vector problem arising in radiation therapy planningJul 01 2009Mar 11 2010In this paper we consider the problem of finding a vector that can be written as a nonnegative integer linear combination of given 0-1 vectors, the generators, such that the l_1-distance between this vector and a given target vector is minimized. We prove ... More

Minimum Entropy Combinatorial Optimization ProblemsAug 17 2010We survey recent results on combinatorial optimization problems in which the objective function is the entropy of a discrete distribution. These include the minimum entropy set cover, minimum entropy orientation, and minimum entropy coloring problems. ... More

Minimum Entropy OrientationsFeb 09 2008Sep 22 2008We study graph orientations that minimize the entropy of the in-degree sequence. The problem of finding such an orientation is an interesting special case of the minimum entropy set cover problem previously studied by Halperin and Karp [Theoret. Comput. ... More

Weighted graphs defining facets: a connection between stable set and linear ordering polytopesSep 22 2008A graph is alpha-critical if its stability number increases whenever an edge is removed from its edge set. The class of alpha-critical graphs has several nice structural properties, most of them related to their defect which is the number of vertices ... More

Strengthening Convex Relaxations of 0/1-Sets Using Boolean FormulasNov 03 2017Jun 23 2018In convex integer programming, various procedures have been developed to strengthen convex relaxations of sets of integer points. On the one hand, there exist several general-purpose methods that strengthen relaxations without specific knowledge of the ... More

Small Extended Formulation for Knapsack Cover Inequalities from Monotone CircuitsSep 13 2016Initially developed for the min-knapsack problem, the knapsack cover inequalities are used in the current best relaxations for numerous combinatorial optimization problems of covering type. In spite of their widespread use, these inequalities yield linear ... More

Characterizing Polytopes Contained in the $0/1$-Cube with Bounded Chvátal-Gomory RankNov 20 2016Let $S \subseteq \{0,1\}^n$ and $R$ be any polytope contained in $[0,1]^n$ with $R \cap \{0,1\}^n = S$. We prove that $R$ has bounded Chv\'atal-Gomory rank (CG-rank) provided that $S$ has bounded pitch and bounded gap, where the pitch is the minimum integer ... More

The Price of Connectivity for Vertex CoverMar 11 2013May 15 2013The vertex cover number of a graph is the minimum number of vertices that are needed to cover all edges. When those vertices are further required to induce a connected subgraph, the corresponding number is called the connected vertex cover number, and ... More

Extended formulations, non-negative factorizations and randomized communication protocolsMay 20 2011May 13 2013An extended formulation of a polyhedron $P$ is a linear description of a polyhedron $Q$ together with a linear map $\pi$ such that $\pi(Q)=P$. These objects are of fundamental importance in polyhedral combinatorics and optimization theory, and the subject ... More

Smaller Extended Formulations for the Spanning Tree Polytope of Bounded-genus GraphsApr 27 2016We give an $O(g^{1/2} n^{3/2} + g^{3/2} n^{1/2})$-size extended formulation for the spanning tree polytope of an $n$-vertex graph embedded on a surface of genus $g$, improving on the known $O(n^2 + g n)$-size extended formulations following from Wong ... More

Combinatorial Bounds on Nonnegative Rank and Extended FormulationsNov 02 2011Jul 09 2012An extended formulation of a polytope P is a polytope Q which can be projected onto P. Extended formulations of small size (i.e., number of facets) are of interest, as they allow to model corresponding optimization problems as linear programs of small ... More

Small Extended Formulation for Knapsack Cover Inequalities from Monotone CircuitsSep 13 2016Nov 18 2016Initially developed for the min-knapsack problem, the knapsack cover inequalities are used in the current best relaxations for numerous combinatorial optimization problems of covering type. In spite of their widespread use, these inequalities yield linear ... More

Small Minors in Dense GraphsMay 06 2010Mar 06 2012A fundamental result in structural graph theory states that every graph with large average degree contains a large complete graph as a minor. We prove this result with the extra property that the minor is small with respect to the order of the whole graph. ... More

The VPN Tree Routing Conjecture for Outerplanar NetworksNov 16 2007Nov 24 2008The VPN Tree Routing Conjecture is a conjecture about the Virtual Private Network Design problem. It states that the symmetric version of the problem always has an optimum solution which has a tree-like structure. In recent work, Hurkens, Keijsper and ... More

Smaller Extended Formulations for the Spanning Tree Polytope of Bounded-genus GraphsApr 27 2016Jan 09 2017We give an $O(g^{1/2} n^{3/2} + g^{3/2} n^{1/2})$-size extended formulation for the spanning tree polytope of an $n$-vertex graph embedded on a surface of genus $g$, improving on the known $O(n^2 + g n)$-size extended formulations following from Wong ... More

A note on the Cops & Robber game on graphs embedded in non-orientable surfacesMar 04 2008Feb 04 2011The Cops and Robber game is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if they can catch the robber. The minimum number of cops needed to win on a ... More

Small Extended Formulations for Cyclic PolytopesJan 31 2014Feb 20 2015We provide an extended formulation of size O(log n)^{\lfloor d/2 \rfloor} for the cyclic polytope with dimension d and n vertices (i,i^2,\ldots,i^d), i in [n]. First, we find an extended formulation of size log(n) for d= 2. Then, we use this as base case ... More

Unavoidable minors for graphs with large $\ell_p$-dimensionApr 05 2019A metric graph is a pair $(G,d)$, where $G$ is a graph and $d:E(G) \to\mathbb{R}_{\geq0}$ is a distance function. Let $p \in [1,\infty]$ be fixed. An isometric embedding of the metric graph $(G,d)$ in $\ell_p^k = (\mathbb{R}^k, d_p)$ is a map $\phi : ... More

Unavoidable minors for graphs with large $\ell_p$-dimensionApr 05 2019Apr 26 2019A metric graph is a pair $(G,d)$, where $G$ is a graph and $d:E(G) \to\mathbb{R}_{\geq0}$ is a distance function. Let $p \in [1,\infty]$ be fixed. An isometric embedding of the metric graph $(G,d)$ in $\ell_p^k = (\mathbb{R}^k, d_p)$ is a map $\phi : ... More

No Small Linear Program Approximates Vertex Cover within a Factor $2 - ε$Mar 02 2015Nov 26 2015The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems. Khot and Regev (2003) proved that the problem is NP-hard to approximate within a factor $2 - \epsilon$, assuming the Unique Games Conjecture ... More

Generalised probabilistic theories and conic extensions of polytopesOct 15 2013Jun 30 2014Generalized probabilistic theories (GPT) provide a general framework that includes classical and quantum theories. It is described by a cone $C$ and its dual $C^*$. We show that whether some one-way communication complexity problems can be solved within ... More

The excluded minors for isometric realizability in the planeNov 25 2015Sep 16 2016Let $G$ be a graph and $p \in [1, \infty]$. The parameter $f_p(G)$ is the least integer $k$ such that for all $m$ and all vectors $(r_v)_{v \in V(G)} \subseteq \mathbb{R}^m$, there exist vectors $(q_v)_{v \in V(G)} \subseteq \mathbb{R}^k$ satisfying $$\|r_v-r_w\|_p=\|q_v-q_w\|_p, ... More

Extension complexity of stable set polytopes of bipartite graphsFeb 28 2017Jun 05 2017The extension complexity $\mathsf{xc}(P)$ of a polytope $P$ is the minimum number of facets of a polytope that affinely projects to $P$. Let $G$ be a bipartite graph with $n$ vertices, $m$ edges, and no isolated vertices. Let $\mathsf{STAB}(G)$ be the ... More

Characterizing Polytopes Contained in the $0/1$-Cube with Bounded Chvátal-Gomory RankNov 20 2016Nov 07 2017Let $S \subseteq \{0,1\}^n$ and $R$ be any polytope contained in $[0,1]^n$ with $R \cap \{0,1\}^n = S$. We prove that $R$ has bounded Chv\'atal-Gomory rank (CG-rank) provided that $S$ has bounded notch and bounded gap, where the notch is the minimum integer ... More

A $\frac{3}{2}$-Approximation Algorithm for Tree Augmentation via Chvátal-Gomory CutsFeb 18 2017Feb 23 2017The weighted tree augmentation problem (WTAP) is a fundamental network design problem. We are given an undirected tree $G = (V,E)$, an additional set of edges $L$ called links and a cost vector $c \in \mathbb{R}^L_{\geq 1}$. The goal is to choose a minimum ... More

Approximation Limits of Linear Programs (Beyond Hierarchies)Apr 04 2012May 16 2014We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any linear program ... More

Extension Complexity of the Correlation PolytopeJun 01 2018Oct 18 2018We prove that for every $n$-vertex graph $G$, the extension complexity of the correlation polytope of $G$ is $2^{O(\mathrm{tw}(G) + \log n)}$, where $\mathrm{tw}(G)$ is the treewidth of $G$. Our main result is that this bound is tight for graphs contained ... More

The Stackelberg Minimum Spanning Tree GameMar 05 2007Sep 17 2009We consider a one-round two-player network pricing game, the Stackelberg Minimum Spanning Tree game or StackMST. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges have a given fixed ... More

Extended Formulations for Order Polytopes through Network FlowsOct 07 2017Mathematical psychology has a long tradition of modeling probabilistic choice via distribution-free random utility models and associated random preference models. For such models, the predicted choice probabilities often form a bounded and convex polyhedral ... More

A tight Erdős-Pósa function for wheel minorsOct 17 2017Jul 05 2018Let $W_t$ denote the wheel on $t+1$ vertices. We prove that for every integer $t \geq 3$ there is a constant $c=c(t)$ such that for every integer $k\geq 1$ and every graph $G$, either $G$ has $k$ vertex-disjoint subgraphs each containing $W_t$ as minor, ... More

Sorting under Partial Information (without the Ellipsoid Algorithm)Oct 31 2009Jan 21 2013We revisit the well-known problem of sorting under partial information: sort a finite set given the outcomes of comparisons between some pairs of elements. The input is a partially ordered set P, and solving the problem amounts to discovering an unknown ... More

Enumeration of $2$-level polytopesMar 06 2017Mar 31 2017A (convex) polytope $P$ is said to be $2$-level if for every direction of hyperplanes which is facet-defining for $P$, the vertices of $P$ can be covered with two hyperplanes of that direction. The study of these polytopes is motivated by questions in ... More

An Efficient Algorithm for Partial Order ProductionNov 17 2008Dec 01 2009We consider the problem of partial order production: arrange the elements of an unknown totally ordered set T into a target partially ordered set S, by comparing a minimum number of pairs in T. Special cases include sorting by comparisons, selection, ... More

Exponential Lower Bounds for Polytopes in Combinatorial OptimizationNov 03 2011Mar 13 2015We solve a 20-year old problem posed by Yannakakis and prove that there exists no polynomial-size linear program (LP) whose associated polytope projects to the traveling salesman polytope, even if the LP is not required to be symmetric. Moreover, we prove ... More

The Stackelberg Minimum Spanning Tree Game on Planar and Bounded-Treewidth GraphsSep 17 2009Sep 13 2011The Stackelberg Minimum Spanning Tree Game is a two-level combinatorial pricing problem played on a graph representing a network. Its edges are colored either red or blue, and the red edges have a given fixed cost, representing the competitor's prices. ... More

A special case of the $Γ_{00}$ conjectureApr 03 2008Sep 02 2010In this paper we prove the $\Gamma_{00}$ conjecture of van Geemen and van der Geer, under the additional assumption that the matrix of coefficients of the tangent has rank at most 2. This assumption is satisfied by Jacobians, and thus our result gives ... More

Convergence of the Yang-Mills-Higgs flow on gauged holomorphic maps and applicationsOct 07 2016The symplectic vortex equations admit a variational description as global minimum of the Yang--Mills--Higgs functional. We study its negative gradient flow on holomorphic pairs $(A,u)$ where $A$ is a connection on a principal $G$-bundle $P$ over a closed ... More

On Certain Tilting Modules for SL2May 19 2017Sep 19 2017We give a complete picture of when the tensor product of an induced module and a Weyl module is a tilting module for the algebraic group $SL_2$ over an algebraically closed field of characteristic $p$. Whilst the result is recursive by nature, we give ... More

A Dichotomy in Machine KnowledgeAug 04 2011We show that a machine, which knows basic logic and arithmetic and basic axioms of knowledge, and which is factive (knows nothing false), can either know that it is factive, or know its own Goedel number, but not both.

Characterisations of purity in a locally finitely presented additive category: A short functorial proofFeb 23 2017In this short note, we will give an efficient functorial proof of the equivalence of various characterisations of purity in a locally finitely presented additive category $C$. The complications of the proofs for specific choices of $C$ (e.g. $C=A\text{-Mod}$ ... More

Ioana's superrigidity theorem and orbit equivalence relationsOct 09 2013Dec 31 2013In this expository article, we give a survey of Adrian Ioana's cocycle superrigidity theorem for profinite actions of Property (T) groups, and its applications to ergodic theory and set theory. In addition to a statement and proof of Ioana's theorem, ... More

A theoretical framework for retinal computations: insights from textbook knowledgeJun 07 2018Neural circuits in the retina divide the incoming visual scene into more than a dozen distinct representations that are sent on to central brain areas, such as the lateral geniculate nucleus and the superior colliculus. The retina can be viewed as a parallel ... More

A quantum point contact as a (near) perfect spin polariserNov 28 2018In this paper, I present a simple method of obtaining spin-polarised current from a QPC with a large Rashba interaction. The origin of this spin polarisation is the adiabatic evolution of spin "up" of the first QPC sub-band, into spin "down" of the second ... More

Propagation in media as a probe for topological propertiesSep 23 2017The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete classification of ... More

A Sequent Calculus for Dynamic Topological LogicJul 25 2014Aug 03 2014We introduce a sequent calculus for the temporal-over-topological fragment $\textbf{DTL}_{0}^{\circ * \slash \Box}$ of dynamic topological logic $\textbf{DTL}$, prove soundness semantically, and prove completeness syntactically using the axiomatization ... More

Escaping the Tragedy of the Commons through Targeted PunishmentJun 04 2015Failures of cooperation cause many of society's gravest problems. It is well known that cooperation among many players faced with a social dilemma can be maintained thanks to the possibility of punishment, but achieving the initial state of widespread ... More

Interplay between Network Topology and Dynamics in Neural SystemsFeb 16 2013This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes, can shape the ... More

Complexity of comparing monomials and two improvements of the BM-algorithmJul 15 2008Aug 27 2008We give a new algorithm for merging sorted lists of monomials. Together with a projection technique we obtain a new complexity bound for the BM-algorithm.

On weighted optimality of experimental designsOct 20 2016When the experimental objective is expressed by a set of estimable functions, and any eigenvalue-based optimality criterion is selected, we prove the equivalence of the recently introduced weighted optimality and the 'standard' optimality criteria for ... More

Real-Time Multiple Object Tracking - A Study on the Importance of SpeedSep 11 2017Oct 02 2017In this project, we implement a multiple object tracker, following the tracking-by-detection paradigm, as an extension of an existing method. It works by modelling the movement of objects by solving the filtering problem, and associating detections with ... More

Simple fixed-brane gauges in $S_1/Z_2$ braneworldsApr 07 2006For five-dimensional braneworlds with an $S_1/\mathbb{Z}_2$ orbifold topology for the extra dimension $x^5$, we discuss the validity of recent claims that a gauge exists where the two boundary branes lie at fixed positions and the metric satisfies $g_{\mu ... More

Twisted Spin in Quantum MechanicsJul 01 2019In quantum mechanics, spin is quantized. It is often thought that the spin of an object points in a fixed direction at any point in time. For example, after selecting the z-direction as the axis of quantization, a spin 1/2 object (such as an electron) ... More

The number of points from a random lattice that lie inside a ballNov 12 2013We prove a sharp bound for the remainder term of the number of lattice points inside a ball, when averaging over a compact set of (not necessarily unimodular) lattices, in dimensions two and three. We also prove that such a bound cannot hold if one averages ... More

Chern classes of the tangent bundle on the Hilbert scheme of points on the affine planeOct 21 2004Mar 31 2005The cohomology of the Hilbert schemes of points on smooth projective surfaces can be approached both with vertex algebra tools and equivariant tools. Using the first tool, we study the existence and the structure of universal formulas for the Chern classes ... More

Infinitesimal thickenings of Morava K-theoriesJul 05 2006Mar 06 2008A. Baker has constructed certain sequences of cohomology theories which interpolate between the Johnson-Wilson and the Morava K-theories. We realize the representing sequences of spectra as sequences of MU-algebras. Starting with the fact that the spectra ... More

I-adic towers in topologyNov 18 2004Nov 30 2005A large variety of cohomology theories is derived from complex cobordism MU^*(-) by localizing with respect to certain elements or by killing regular sequences in MU_*. We study the relationship between certain pairs of such theories which differ by a ... More

Infinite graphs in systematic biology, with an application to the species problemJan 13 2012Dec 13 2012We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs ... More

New classes of null hypersurfaces in indefinite Sasakian space-formsJul 10 2019We introduce two classes of null hypersurfaces of an indefinite Sasakian manifold, $(\overline{M}, \overline{\phi},\zeta, \eta)$, tangent to the characteristic vector field $\zeta$, called; {\it contact screen conformal} and {\it contact screen umbilic} ... More

Almost prime values of the order of abelian varieties over finite fieldsMar 09 2018Let $E/\mathbb Q$ be an elliptic curve, and denote by $N(p)$ the number of $\mathbb{F}_p$-points of the reduction modulo $p$ of $E$. A conjecture of Koblitz, refined by Zywina, states that the number of primes $p \leq X$ at which $N(p)$ is also prime ... More

Superstring scattering amplitudes in higher genusMar 24 2008May 20 2008In this paper we continue the program pioneered by D'Hoker and Phong, and recently advanced by Cacciatori, Dalla Piazza, and van Geemen, of finding the chiral superstring measure by constructing modular forms satisfying certain factorization constraints. ... More

Steady periodic gravity waves with surface tensionNov 06 2009In this paper we consider two-dimensional, stratified, steady water waves propagating over an impermeable flat bed and with a free surface. The motion is assumed to be driven by capillarity (that is, surface tension) on the surface and a gravitational ... More

The global anomaly of the self-dual field in general backgroundsSep 25 2013Aug 04 2015We prove a formula for the global gravitational anomaly of the self-dual field theory in the presence of background gauge fields, assuming the results of arXiv:1110.4639. Along the way, we also clarify various points about the self-dual field theory. ... More

Randomness Conservation over AlgorithmsJul 11 2013Oct 14 2013Current discrete randomness and information conservation inequalities are over total recursive functions, i.e. restricted to deterministic processing. This restriction implies that an algorithm can break algorithmic randomness conservation inequalities. ... More

Presenting Finite PosetsMay 27 2015We introduce a monoidal category whose morphisms are finite partial orders, with chosen minimal and maximal elements as source and target respectively. After recalling the notion of presentation of a monoidal category by the means of generators and relations, ... More

The defect recollement, the MacPherson-Vilonen construction, and pp formulasAug 19 2018Dec 23 2018For any abelian category $\mathcal{A}$, Auslander constructed a localisation $w:\mathrm{fp}(\mathcal{A}^{\mathrm{op}},\mathrm{Ab})\to \mathcal{A}$ called the defect, which is the left adjoint to the Yoneda embedding $Y:\mathcal{A}\to\mathrm{fp}(\mathcal{A}^{\mathrm{op}},\mathrm{Ab})$. ... More

Gravity and decoherence: the double slit experiment revisitedJun 14 2017Jan 29 2018The double slit experiment is iconic and widely used in classrooms to demonstrate the fundamental mystery of quantum physics. The puzzling feature is that the probability of an electron arriving at the detector when both slits are open is not the sum ... More

The classification of torsion-free abelian groups of finite rank up to isomorphism and up to quasi-isomorphismFeb 07 2009The isomorphism and quasi-isomorphism relations on the $p$-local torsion-free abelian groups of rank $n\geq3$ are incomparable with respect to Borel reducibility.

Some Notes on Temporal Justification LogicOct 25 2015Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal ... More

Graphes, moyennabilité et bas du spectre de variétés topologiquement infiniesJan 14 2010From a graph $G$ with constant valency $v$ and a (non-compact) manifold $C$ with $v$ boundary components, we build a $G$-periodic manifold $M$. This process gives a class of topologically infinite manifolds which generalizes periodic manifolds and includes ... More

Generic metrics, eigenfunctions and riemannian coverings of non compact manifoldsJan 14 2010Let $(M,g)$ be a non-compact riemannian $n$-manifold with bounded geometry at order $k\geq\frac{n}{2}$. We show that if the spectrum of the Laplacian starts with $q+1$ discrete eigenvalues isolated from the essential spectrum, and if the metric is generic ... More

A type of simulation which some experimental evidence suggests we don't live inJul 03 2018Do we live in a computer simulation? I will present an argument that the results of a certain experiment constitute empirical evidence that we do not live in, at least, one type of simulation. The type of simulation ruled out is very specific. Perhaps ... More

On Arrangements of Six, Seven, and Eight Spheres: Maximal Bonding of Monatomic Ionic CompoundsMar 27 2016Let $C(n)$ be the solution to the contact number problem, i.e., the maximum number of touching pairs among any packing of $n$ congruent spheres in $\mathbb{R}^3$. We prove the long conjectured values of $C(6)=12, C(7)=15$, and $C(8)=18$. The proof strategy ... More

General Linear and Symplectic Nilpotent Orbit VarietiesMar 12 2014The condition of nilpotency is studied in the general linear Lie algebra $\mathfrak{gl}_{n}(\mathbb{K})$ and the symplectic Lie algebra $\mathfrak{sp}_{2m}(\mathbb{K})$ over an algebraically closed field of characteristic 0. In particular, the conjugacy ... More

Global gravitational anomaly cancellation for five-branesOct 08 2013Nov 07 2014We show that the global mixed gauge-gravitational anomaly of the worldvolume theory of the M5-brane vanishes, when the anomaly inflow from the bulk is taken into account. This result extends to the type IIA and heterotic $E_8 \times E_8$ five-branes. ... More

Some criteria for the symmetry of stratified water wavesMar 05 2009This paper considers two-dimensional stably stratified steady periodic gravity water waves with surface profiles monotonic between crests and troughs. We provide sufficient conditions under which such waves are necessarily symmetric. This is done by first ... More

E- and R-optimality of block designs for treatment-control comparisonsApr 18 2018We study optimal block designs for comparing a set of test treatments with a control treatment. We provide the class of all E-optimal approximate block designs characterized by simple linear constraints. Employing this characterization, we obtain a class ... More

Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular casesAug 20 2014Jan 16 2015The modified algebraic Bethe ansatz, introduced by Cramp\'e and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-$\frac{1}{2}$ chain on the segment with lower and upper triangular boundaries. The eigenvalues and ... More

Regular Totally Separable Sphere PackingsJun 06 2015The topic of totally separable sphere packings is surveyed with a focus on regular constructions, uniform tilings, and contact number problems. An enumeration of all regular totally separable sphere packings in $\mathbb{R}^2$, $\mathbb{R}^3$, and $\mathbb{R}^4$ ... More

Topological field theories on manifolds with Wu structuresJul 05 2016Aug 09 2018We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we gauge it, producing ... More

A Small Model for the Cohomology of Some Principal BundlesSep 25 2013Let G be a compact, connected and simply connected Lie group, and {\Omega}G the space of the loops in G based at the identity. This note shows a way to compute the cohomology of the total space of a principal {\Omega}G-bundle over a manifold M, from the ... More

Duality and contravariant functors in the representation theory of artin algebrasMar 18 2016Feb 23 2017We know that the model theory of modules leads to a way of obtaining definable categories of modules over a ring $R$ as the kernels of certain functors $(R\textbf{-Mod})^{\text{op}}\to\textbf{Ab}$ rather than of functors $R\textbf{-Mod}\to\textbf{Ab}$ ... More

Hamiltonian anomalies from extended field theoriesOct 27 2014Jan 10 2019We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down ... More

On Generalizing a Temporal Formalism for Game Theory to the Asymptotic Combinatorics of S5 Modal FramesMay 01 2013A temporal-theoretic formalism for understanding game theory is described where a strict ordering relation on a set of time points $T$ defines a game on $T$. Using this formalism, a proof of Zermelo's Theorem, which states that every finite 2-player zero-sum ... More

Dynamics on dendrites with closed endpoint setsJul 03 2019We construct dendrites with endpoint sets isometric to any totally disconnected compact metric space. This allows us to embed zero-dimensional dynamical systems into dendrites and solve a problem regarding Li-Yorke and distributional chaos.

A gluing theorem for negatively curved complexesOct 09 2015Jul 09 2016A simplicial complex is called negatively curved if all its simplices are isometric to simplices in hyperbolic space, and it satisfies Gromov's Link Condition. We prove that, subject to certain conditions, a compact graph of spaces whose vertex spaces ... More

Veech surfaces associated with rational billiardsMay 23 2002A nice trick for studying the billiard flow in a rational polygon is to unfold the polygon along the trajectories. This gives rise to a translation or half-translation surface tiled by the original polygon, or equivalently an Abelian or quadratic differential. ... More

Cubic equations for the hyperelliptic locusMar 02 2005We discuss the conjecture of Buchstaber and Krichever that their multi-dimensional vector addition formula for Baker-Akhiezer functions characterizes Jacobians among principally polarized abelian varieties, and prove that it is indeed a weak characterization, ... More