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Optimal Mechansim Design and Money BurningApr 14 2008Mechanism design is now a standard tool in computer science for aligning the incentives of self-interested agents with the objectives of a system designer. There is, however, a fundamental disconnect between the traditional application domains of mechanism ... More

An End-to-end Argument in Mechanism Design (Prior-independent Auctions for Budgeted Agents)Apr 05 2018Jul 30 2018This paper considers prior-independent mechanism design, namely identifying a single mechanism that has near optimal performance on every prior distribution. We show that mechanisms with truthtelling equilibria, a.k.a., revelation mechanisms, do not always ... More

Optimal Auctions vs. Anonymous Pricing: Beyond Linear UtilityMay 10 2019The revenue optimal mechanism for selling a single item to agents with independent but non-identically distributed values is complex for agents with linear utility (Myerson,1981) and has no closed-form characterization for agents with non-linear utility ... More

Multi-dimensional Virtual Values and Second-degree Price DiscriminationApr 04 2014Aug 24 2015We consider a multi-dimensional screening problem of selling a product with multiple quality levels and design virtual value functions to derive conditions that imply optimality of only selling highest quality. A challenge of designing virtual values ... More

Non-Revelation Mechanism DesignAug 05 2016We consider mechanism design and redesign for markets like Internet advertising where many frequent, small transactions are organized by a principal. Mechanisms for these markets rarely have truthtelling equilibria. We identify a family of winner-pays-bid ... More

Optimal Platform DesignDec 30 2014An auction house cannot generally provide the optimal auction technology to every client. Instead it provides one or several auction technologies, and clients select the most appropriate one. For example, eBay provides ascending auctions and "buy-it-now" ... More

Bayesian Budget Feasibility with Posted PricingJun 12 2015Oct 21 2015We consider the problem of budget feasible mechanism design proposed by Singer (2010), but in a Bayesian setting. A principal has a public value for hiring a subset of the agents and a budget, while the agents have private costs for being hired. We consider ... More

Bayesian Algorithmic Mechanism DesignSep 25 2009Feb 23 2011The principal problem in algorithmic mechanism design is in merging the incentive constraints imposed by selfish behavior with the algorithmic constraints imposed by computational intractability. This field is motivated by the observation that the preeminent ... More

Mechanism Design for Data ScienceApr 23 2014Jun 09 2014Good economic mechanisms depend on the preferences of participants in the mechanism. For example, the revenue-optimal auction for selling an item is parameterized by a reserve price, and the appropriate reserve price depends on how much the bidders are ... More

No-Regret Learning in Bayesian GamesJul 02 2015Nov 19 2015Recent price-of-anarchy analyses of games of complete information suggest that coarse correlated equilibria, which characterize outcomes resulting from no-regret learning dynamics, have near-optimal welfare. This work provides two main technical results ... More

Prior-independent Auctions for Risk-averse AgentsJan 03 2013We study simple and approximately optimal auctions for agents with a particular form of risk-averse preferences. We show that, for symmetric agents, the optimal revenue (given a prior distribution over the agent preferences) can be approximated by the ... More

Optimal Crowdsourcing ContestsNov 12 2011We study the design and approximation of optimal crowdsourcing contests. Crowdsourcing contests can be modeled as all-pay auctions because entrants must exert effort up-front to enter. Unlike all-pay auctions where a usual design objective would be to ... More

Mechanism Design via Consensus Estimates, Cross Checking, and Profit ExtractionAug 24 2011There is only one technique for prior-free optimal mechanism design that generalizes beyond the structurally benevolent setting of digital goods. This technique uses random sampling to estimate the distribution of agent values and then employs the Bayesian ... More

Mechanism RedesignAug 15 2017This paper develops the theory of mechanism redesign by which an auctioneer can reoptimize an auction based on bid data collected from previous iterations of the auction on bidders from the same market. We give a direct method for estimation of the revenue ... More

Price of Anarchy for Auction RevenueApr 23 2014Jun 09 2014This paper develops tools for welfare and revenue analyses of Bayes-Nash equilibria in asymmetric auctions with single-dimensional agents. We employ these tools to derive price of anarchy results for social welfare and revenue. Our approach separates ... More

A/B Testing of AuctionsJun 02 2016For many application areas A/B testing, which partitions users of a system into an A (control) and B (treatment) group to experiment between several application designs, enables Internet companies to optimize their services to the behavioral patterns ... More

The Biased Sampling Profit Extraction AuctionJun 21 2012We give an auction for downward-closed environments that generalizes the random sampling profit extraction auction for digital goods of Fiat et al. (2002). The mechanism divides the agents in to a market and a sample using a biased coin and attempts to ... More

Optimal Auctions for Correlated Buyers with SamplingJun 06 2014Cr\'emer and McLean [1985] showed that, when buyers' valuations are drawn from a correlated distribution, an auction with full knowledge on the distribution can extract the full social surplus. We study whether this phenomenon persists when the auctioneer ... More

Envy Freedom and Prior-free Mechanism DesignDec 16 2012We consider the provision of an abstract service to single-dimensional agents. Our model includes position auctions, single-minded combinatorial auctions, and constrained matching markets. When the agents' values are drawn from a distribution, the Bayesian ... More

Prior-Independent Mechanisms for SchedulingMay 02 2013We study the makespan minimization problem with unrelated selfish machines under the assumption that job sizes are stochastic. We design simple truthful mechanisms that under various distributional assumptions provide constant and sublogarithmic approximations ... More

Inference from Auction PricesFeb 19 2019Econometric inference allows an analyst to back out the values of agents in a mechanism from the rules of the mechanism and bids of the agents. This paper proposes the problem of inferring the values of agents in a mechanism from the social choice function ... More

Bayesian Optimal Auctions via Multi- to Single-agent ReductionMar 22 2012We study an abstract optimal auction problem for a single good or service. This problem includes environments where agents have budgets, risk preferences, or multi-dimensional preferences over several possible configurations of the good (furthermore, ... More

Optimal Auctions vs. Anonymous PricingJul 09 2015For selling a single item to agents with independent but non-identically distributed values, the revenue optimal auction is complex. With respect to it, Hartline and Roughgarden (2009) showed that the approximation factor of the second-price auction with ... More

Dashboard Mechanisms for Online MarketplacesMay 14 2019This paper gives a theoretical model for design and analysis of mechanisms for online marketplaces where a bidding dashboard enables the bid-optimization of long-lived agents. We assume that a good allocation algorithm exists when given the true values ... More

A Truthful Cardinal Mechanism for One-Sided MatchingMar 19 2019We consider the design of randomized mechanisms for one-sided matching markets, where each agent is matched to one item and there are no monetary transfers. For this problem, we introduce and analyze the randomized partial improvement (RPI) mechanism. ... More

The Simple Economics of Approximately Optimal AuctionsJun 15 2012Jun 05 2014The intuition that profit is optimized by maximizing marginal revenue is a guiding principle in microeconomics. In the classical auction theory for agents with linear utility and single-dimensional preferences, Bulow and Roberts (1989) show that the optimal ... More

Prior-free Auctions for Budgeted AgentsDec 23 2012We consider prior-free auctions for revenue and welfare maximization when agents have a common budget. The abstract environments we consider are ones where there is a downward-closed and symmetric feasibility constraint on the probabilities of service ... More

Finding Bidder-Optimal Core Points QuicklyOct 11 2016In complex combinatorial markets with complementary valuations, truthful auctions can yield low revenue. Core-selecting auctions attempt to boost revenue by setting prices so that no group of agents, including the auctioneer, can jointly improve their ... More

Sequential Posted Pricing and Multi-parameter Mechanism DesignJul 14 2009Jan 15 2010We consider the classical mathematical economics problem of {\em Bayesian optimal mechanism design} where a principal aims to optimize expected revenue when allocating resources to self-interested agents with preferences drawn from a known distribution. ... More

Fast Core Pricing for Rich Advertising AuctionsOct 11 2016Mar 08 2018As online ad offerings become increasingly complex, with multiple size configurations and layouts available to advertisers, the sale of web advertising space increasingly resembles a combinatorial auction with complementarities. Standard ad auction formats ... More

A new cohomological formula for helicity in $\R^{2k+1}$ reveals the effect of a diffeomorphism on helicityMar 08 2009Oct 26 2012The helicity of a vector field is a measure of the average linking of pairs of integral curves of the field. Computed by a six-dimensional integral, it is widely useful in the physics of fluids. For a divergence-free field tangent to the boundary of a ... More

Dialog-based Language LearningApr 20 2016Aug 23 2016A long-term goal of machine learning research is to build an intelligent dialog agent. Most research in natural language understanding has focused on learning from fixed training sets of labeled data, with supervision either at the word level (tagging, ... More

The geometry of cyclic hyperbolic polygonsJan 25 2011Jun 30 2015A hyperbolic polygon is defined to be cyclic, horocyclic, or equidistant if its vertices lie on a metric circle, horocycle, or a component of the equidistant locus to a hyperbolic geodesic, respectively. Convex such $n$-gons are parametrized by the subspaces ... More

A sharp analysis of the mixing time for random walk on rooted treesAug 08 2009We define an analog of Plancherel measure for the set of rooted unlabeled trees on n vertices, and a Markov chain which has this measure as its stationary distribution. Using the combinatorics of commutation relations, we show that order n^2 steps are ... More

Commutation relations and Markov chainsDec 09 2007Jan 20 2008It is shown that the combinatorics of commutation relations is well suited for analyzing the convergence rate of certain Markov chains. Examples studied include random walk on irreducible representations, a local random walk on partitions whose stationary ... More

An Inductive Proof of the Berry-Esseen Theorem for Character RatiosMar 11 2005Aug 08 2006Bolthausen used a variation of Stein's method to give an inductive proof of the Berry-Esseen theorem for sums of independent, identically distributed random variables. We modify this technique to prove a Berry-Esseen theorem for character ratios of a ... More

Stein's Method and Minimum Parsimony Distance after ShufflesOct 29 2004Motivated by Bourque and Pevzner's simulation study of the parsimony method for studying genome rearrangement, Berestycki and Durrett used techniques from random graph theory to prove that the minimum parsimony distance after iterating the random transposition ... More

A New Bound for Kloosterman SumsMay 22 2001Jun 21 2001We give generating functions for Gauss sums for finite general linear and unitary groups. For the general linear case only our method of proof is new, but we deduce a bound on Kloosterman sums which is sometimes sharper than Deligne's bound from algebraic ... More

Applications of the Brauer complex: card shuffling, permutation statistics, and dynamical systemsFeb 14 2001May 09 2001By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes ... More

A Probabilistic Proof of the Rogers Ramanujan IdentitiesJan 13 2000Nov 21 2000The asymptotic probability theory of conjugacy classes of the finite general linear and unitary groups leads to a probability measure on the set of all partitions of natural numbers. A simple method of understanding these measures in terms of Markov chains ... More

Stein's method, heat kernel, and traces of powers of elements of compact Lie groupsMay 07 2010Combining Stein's method with heat kernel techniques, we show that the trace of the jth power of an element of U(n,C), USp(n,C) or SO(n,R) has a normal limit with error term of order j/n. In contrast to previous works, here j may be growing with n. The ... More

Short lists for shortest descriptions in short timeDec 26 2012Feb 12 2014Is it possible to find a shortest description for a binary string? The well-known answer is "no, Kolmogorov complexity is not computable." Faced with this barrier, one might instead seek a short list of candidates which includes a laconic description. ... More

Stillman's Question for Exterior AlgebrasJul 30 2013Let K be any field and consider exterior algebras of a finite dimensional K-vector space. In this very short paper we exhibit principal quadric ideals in a family whose Castelnuovo Mumford regularity is unbounded.

Determining the velocity dispersion of the thick discMay 24 2012Jul 23 2012We attempt to recover the mean vertical velocity and vertical velocity dispersion as a function of the Galactic height for a sample drawn from a realistic Galaxy distribution function by following the method presented in Moni Bidin et al. (2012). We find ... More

Stability of Infinite Systems of Coupled Oscillators Via Random Walks on Weighted GraphsMay 06 2018Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a canonical phase ... More

Efficient Normal-Form Parsing for Combinatory Categorial GrammarJun 02 1996Under categorial grammars that have powerful rules like composition, a simple n-word sentence can have exponentially many parses. Generating all parses is inefficient and obscures whatever true semantic ambiguities are in the input. This paper addresses ... More

Coupling the Dirac and Einstein equations through geometryMar 28 2019We show that the Clifford bundle over a curved spacetime can be used as framework in which both the Dirac and the Einstein equations can be obtained. These equations, and their coupling, follow from the variational principle applied to a Lagrangian constructed ... More

Speculative Parallel Evaluation Of Classification Trees On GPGPU Compute EnginesNov 06 2011We examine the problem of optimizing classification tree evaluation for on-line and real-time applications by using GPUs. Looking at trees with continuous attributes often used in image segmentation, we first put the existing algorithms for serial and ... More

Estimation of the r-th derivative of a density function by the tilted kernel estimatorOct 27 2015We consider the problem of estimating the s-th derivative of a density function f by the tilted Kernel estimator introduced in Hall and Doosti (2012). Then we further show this estimator achieves the same convergence rate, in probability, the wavelet ... More

Novel Dark Matter Models and Detection StrategiesOct 11 2012We consider the impact of relaxing some typical assumptions about dark matter interactions, including isospin-invariance, elastic scattering and contact interactions. We show that detection strategies with neutrino detectors, gamma-ray searches, new direct ... More

A Brief Comment on Instanton-like Singularities and Cosmological HorizonsApr 15 2002Apr 27 2002We argue that in the presence of instanton-like singularities, the existence of cosmological horizons can become frame-dependent, ie. a horizon which appears in Einstein frame may not appear in string frame. We speculate on the relation between instanton-like ... More

Deformation Theory of Asymptotically Conical Coassociative 4-foldsNov 05 2004Oct 26 2009We study coassociative 4-folds N in R^7 which are asymptotically conical to a cone C with rate lambda<1. If lambda is in the interval [-2,1) and generic, we show that the moduli space of coassociative deformations of N which are also asymptotically conical ... More

Enhanced $thj$ signal at the LHC with $h\rightarrow γγ$ decay and $\mathcal{CP}$-violating top-Higgs couplingOct 10 2014Apr 03 2015We study the observability of non-standard top Yukawa couplings in the $pp\rightarrow t(\rightarrow \ell \nu_\ell b ) h(\rightarrow \gamma\gamma)j$ channel at 14 TeV high-luminosity LHC (HL-LHC). The small diphoton branching ratio is enhanced when the ... More

On the close interaction between algorithmic randomness and constructive/computable measure theoryDec 08 2018Mar 16 2019This is a survey of constructive and computable measure theory with an emphasis on the close connections with algorithmic randomness. We give a brief history of constructive measure theory from Brouwer to the present, emphasizing how Schnorr randomness ... More

The distribution of r-free numbers in arithmetic progressionsFeb 25 2013A positive integer n is called r-free if n is not divisible by the r-th power of a prime. Generalizing earlier work of Orr, we provide an upper bound of Bombieri-Vinogradov type for the r-free numbers in arithmetic progressions.

Covariant bandlimitation from Generalized Uncertainty PrinciplesMar 28 2019It is widely believed that combining the uncertainty principle with gravity will lead to an effective minimum length scale. A particular challenge is to specify this scale in a coordinate-independent manner so that covariance is not broken. Here we examine ... More

Global existence for semilinear wave equations exterior to nontrapping obstaclesOct 16 2002Feb 21 2003In this paper, we show global existence, in spatial dimensions greater than or equal to four, for semilinear wave equations with quadratic nonlinearities exterior to a nontrapping obstacle. This extends the previous work of Shibata-Tsutsumi and Hayashi. ... More

Global Strichartz Estimates for Solutions to the Wave Equation Exterior to a Convex ObstacleOct 15 2002Jul 20 2004In this paper, we show that certain local Strichartz estimates for solutions of the wave equation exterior to a convex obstacle can be extended to estimates that are global in both space and time. This extends the work that was done previously by H. Smith ... More

Probing the flavor dependence of proton's light-quark sea in the SeaQuest experimentJul 31 2019Surprisingly large flavor asymmetry of the light-quark sea in the proton was reported in deep-inelastic scattering and Drell-Yan experiments. The Bjorken-$x$ dependence of the $\bar{d}/\bar{u}$ ratio extracted from the Fermilab E866 experiment also revealed ... More

Semisimple orbits of Lie algebras and card shuffling on Coxeter groupsMar 02 1999Aug 26 1999Random walk on the chambers of hyperplanes arrangements is used to define a family of card shuffling measures $H_{W,x}$ for a finite Coxeter group W and real $x \neq 0$. By algebraic group theory, there is a map from the semisimple orbits of the adjoint ... More

Fluctuations for the Ginzburg-Landau $\nabla φ$ Interface Model on a Bounded DomainFeb 02 2010Jun 08 2010We study the massless field on $D_n = D \cap \tfrac{1}{n} \Z^2$, where $D \subseteq \R^2$ is a bounded domain with smooth boundary, with Hamiltonian $\CH(h) = \sum_{x \sim y} \CV(h(x) - h(y))$. The interaction $\CV$ is assumed to be symmetric and uniformly ... More

Rationality and the Jordan-Gatti-Viniberghi decompositionJan 19 2012Sep 14 2012We verify the conjecture of [10] and use it to prove that the semisimple parts of the rational Jordan-Kac-Vinberg decompositions of a rational vector all lie in a single rational orbit.

Isomorphisms of some quantum spacesOct 31 2012May 16 2013We consider a series of questions that grew out of determining when two quantum planes are isomorphic. In particular, we consider a similar question for quantum matrix algebras and certain ambiskew polynomial rings. Additionally, we modify a result by ... More

The radial defocusing nonlinear Schrödinger equation in three space dimensionsJan 20 2014We study the defocusing nonlinear Schr\"odinger equation in three space dimensions. We prove that any radial solution that remains bounded in the critical Sobolev space must be global and scatter. In the energy-supercritical setting, we employ a space-localized ... More

A probabilistic approach toward the finite general linear and unitary groupsDec 09 1997Probabilistic algorithms are applied to prove theorems about the finite general linear and unitary groups which are typically proved by techniques such as character theory and Moebius inversion. Among the theorems studied are Steinberg's count of unipotent ... More

A Survey of Exoplanetary Detection TechniquesMay 07 2018Exoplanets, or planets outside our own solar system, have long been of interest to astronomers; however, only in the past two decades have scientists had the technology to characterize and study planets so far away from us. With advanced telescopes and ... More

New Electrochemical Characterization Methods for Nanocomposite Supercapacitor ElectrodesJun 02 2014Apr 19 2016Supercapacitor electrodes fabricated from a nanocomposite consisting of multiwall carbon nanotubes and titanium oxide nanoparticles were characterized electrochemically. Conventional electrochemical characterizations cyclic voltammetry and galvanostatic ... More

Rigorous results for a population model with selection I: evolution of the fitness distributionJul 01 2015We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's fitness by $s_N$. Each individual dies at rate one, and ... More

Torsion pairs and filtrations in abelian categories with tilting objectsFeb 13 2013Given a noetherian abelian category $\mathcal Z$ of homological dimension two with a tilting object $T$, the abelian category $\mathcal Z$ and the abelian category of modules over $\text{End} (T)^{\textit{op}}$ are related by a sequence of two tilts; ... More

Polynomial Bridgeland Stable Objects and Reflexive SheavesDec 19 2011Aug 01 2012On a smooth projective threefold, we show that there are only two isomorphism types for the moduli of stable objects with respect to Bayer's standard polynomial Bridgeland stability - the moduli of Gieseker-stable sheaves and the moduli of PT-stable objects ... More

Dynamics of the evolving Bolthausen-Sznitman coalescentDec 12 2011Consider a population of fixed size that evolves over time. At each time, the genealogical structure of the population can be described by a coalescent tree whose branches are traced back to the most recent common ancestor of the population. As time goes ... More

Baryons: What, When and Where?May 29 2008Jun 12 2008We review the current state of empirical knowledge of the total budget of baryonic matter in the Universe as observed since the epoch of reionization. Our summary examines on three milestone redshifts since the reionization of H in the IGM, z = 3, 1, ... More

A Minimal Subsystem of the Kari-Culik TilingsOct 06 2014Sep 29 2015The Kari-Culik tilings are formed from a set of 13 Wang tiles that tile the plane only aperiodically. They are the smallest known set of Wang tiles to do so and are not as well understood as other examples of aperiodic Wang tiles. We show that the $\mathbb{Z}^2$ ... More

The combinatorics of biased riffle shufflesDec 09 1997This paper studies biased riffle shuffles, first defined by Diaconis, Fill, and Pitman. These shuffles generalize the well-studied Gilbert-Shannon-Reeds shuffle and convolve nicely. An upper bound is given for the time for these shuffles to converge to ... More

Purification and characterization of a novel archaeo-eukaryotic primase from MimivirusAug 29 2016DNA replication is a process which is common to all domains of life yet different replication mechanisms are seen among different organisms. The mechanism by which Acanthamoeba polyphaga mimivirus (APMV) undergoes replication is not characterized. Presence ... More

Dialog-based Language LearningApr 20 2016Sep 28 2016A long-term goal of machine learning research is to build an intelligent dialog agent. Most research in natural language understanding has focused on learning from fixed training sets of labeled data, with supervision either at the word level (tagging, ... More

Explicit rank bounds for cyclic coversOct 29 2013Oct 19 2015Let $M$ be a closed, orientable hyperbolic 3-manifold and $\phi$ a homomorphism of its fundamental group onto $\mathbb{Z}$ that is not induced by a fibration over the circle. For each natural number $n$ we give an explicit lower bound, linear in $n$, ... More

Hall-Littlewood polynomials and Cohen-Lenstra heuristics for Jacobians of random graphsMar 03 2014Cohen-Lenstra heuristics for Jacobians of random graphs give rise to random partitions. We connect these random partitions to the Hall-Littlewood polynomials of symmetric function theory, and use this connection to give combinatorial proofs of properties ... More

Stein's Method and Random Character RatiosAug 16 2005Stein's method is used to prove limit theorems for random character ratios. Tools are developed for four types of structures: finite groups, Gelfand pairs, twisted Gelfand pairs, and association schemes. As one example an error term is obtained for a ... More

A Card Shuffling Analysis of Deformations of the Plancherel Measure of the Symmetric GroupFeb 25 2003We study deformations of the Plancherel measure of the symmetric group by lifting them to the symmetric group and using combinatorics of card shuffling. The existing methods for analyzing deformations of Plancherel measure are not obviously applicable ... More

A Probabilistic Approach to Conjugacy Classes in the Finite Symplectic and Orthogonal GroupsMar 02 2000Nov 06 2000Markov chains are used to give a purely probabilistic way of understanding the conjugacy classes of the finite symplectic and orthogonal groups in odd characteristic. As a corollary of these methods one obtains a probabilistic proof of Steinberg's count ... More

The eigenvalue spacing of a random unipotent matrix in its action on linesMay 24 1999The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach toward other asymptotics. ... More

Stein's Method and Characters of Compact Lie GroupsJun 13 2008Jun 24 2008Stein's method is used to study the trace of a random element from a compact Lie group or symmetric space. Central limit theorems are proved using very little information: character values on a single element and the decomposition of the square of the ... More

Separation cutoffs for random walk on irreducible representationsMar 10 2007Random walk on the irreducible representations of the symmetric and general linear groups is studied. A separation distance cutoff is proved and the exact separation distance asymptotics are determined. A key tool is a method for writing the multiplicities ... More

Card shuffling and the decomposition of tensor productsJul 03 2003Let H be a subgroup of a finite group G. We use Markov chains to quantify how large r should be so that the decomposition of the r tensor power of the representation of G on cosets on H behaves (after renormalization) like the regular representation of ... More

Descent identities, Hessenberg varieties, and the Weil conjecturesDec 09 1997The Weil Conjectures are applied to the Hessenberg Varieties to obtain interesting information about the combinatorics of descents in the symmetric group. Combining this with elementary linear algebra leads to elegant proofs of some identities from the ... More

On the close interaction between algorithmic randomness and constructive/computable measure theoryDec 08 2018This is a survey of constructive and computable measure theory with an emphasis on the close connections with algorithmic randomness. We give a brief history of constructive measure theory from Brouwer to the present, emphasizing how Schnorr randomness ... More

A $2$-compact group as a spetsJun 03 2019Jun 12 2019In 1998 Malle introduced spetses which are mysterious objects with non-real Weyl groups. In algebraic topology, a $p$-compact group $\mathbf{X}$ is a space which is a homotopy-theoretic $p$-local analogue of a compact Lie group. A connected $p$-compact ... More

Asymmetric Dark MatterAug 21 2013Sep 17 2013We review the theoretical framework underlying models of asymmetric dark matter, describe astrophysical constraints which arise from observations of neutron stars, and discuss the prospects for detecting asymmetric dark matter.

WIMPless Dark Matter: Models and SignaturesDec 01 2010We consider experimental signatures of WIMPless dark matter. We focus on models where the WIMPless dark matter candidate is a Majorana fermion, and dark matter scattering is predominantly spin-dependent. These models can be probed by IceCube/DeepCore, ... More

Improving on bold play when the gambler is restrictedDec 18 2004Suppose a gambler starts with a fortune in (0,1) and wishes to attain a fortune of 1 by making a sequence of bets. Assume thay whenever the gambler stakes the amount s, the gambler's fortune increases by s with probability w and decreases by s with probability ... More

When does randomness come from randomness?Aug 20 2015Mar 08 2016A result of Shen says that if $F\colon2^{\mathbb{N}}\rightarrow2^{\mathbb{N}}$ is an almost-everywhere computable, measure-preserving transformation, and $y\in2^{\mathbb{N}}$ is Martin-L\"of random, then there is a Martin-L\"of random $x\in2^{\mathbb{N}}$ ... More

Generalized equivariant homology on simplicial complexesMar 08 2011A careful account is given of generalized equivariant homology theories on the category of topological pairs acted on by a group. In particular, upon restriction to the category of equivariant simplicial complexes, the equivalence of equivariant simplicial ... More

Totally geodesic surfaces and homologyJan 23 2006Apr 23 2009We construct examples of hyperbolic rational homology spheres and hyperbolic knot complements in rational homology spheres containing closed embedded totally geodesic surfaces.

A note on the Brown--Erdős--Sós conjecture in groupsFeb 20 2019Apr 09 2019We show that a dense subset of a sufficiently large group multiplication table contains either a large part of the addition table of the integers modulo some $k$, or the entire multiplication table of a certain large abelian group, as a subgrid. As a ... More

Free Diffusions and Property AOJul 07 2009We consider von Neumann algebras generated by the stationary laws of free stochastic differential equations of the form $dX_t = dS_t -1/2 DV(X_t)$ for a suitably convex multivariate noncommutative polynomial $V$. Using techniques of Guionnet and Shlyakhtenko, ... More

The classification of compact simply connected biquotients in dimension 6 and 7Mar 24 2014Aug 23 2016We classify all compact simply connected biquotients of dimension 6 and 7. For each $6$-dimensional biquotient, all pairs of groups $(G,H)$ and homomorphisms $H\rightarrow G\times G$ giving rise to it are classified.

Rationally $4$-periodic biquotientsMay 25 2016Aug 22 2017An $n$-dimensional manifold $M$ is said to be rationally $4$-periodic if there is an element $e\in H^4(M;\mathbb{Q})$ with the property that cupping with $e$, $\cdot \cup e:H^\ast(M;\mathbb{Q})\rightarrow H^{\ast + 4}(M;\mathbb{Q})$ is injective for $0< ... More

The Doorways Problem and Sturmian WordsMay 01 2017The doorways problem considers adjacent parallel hallways of unit width each with a single doorway (aligned with integer lattice points) of unit width. It then asks, what are the properties of lines that pass through each doorway? Configurations of doorways ... More

A relation between higher-rank PT stable objects and quotients of coherent sheavesOct 02 2018On a smooth projective threefold, we construct an essentially surjective functor $\mathcal{F}$ from a category of two-term complexes to a category of quotients of coherent sheaves, and describe the fibers of this functor. Under a coprime assumption on ... More