tight formulations for some simple mixed integer programs and convex objective integer programs we study the polyhedral structure of simple mixed integer sets that generalize the two variable set s z r 1 z 1 s z b these sets form basic building blocks that can be used to derive tight formulations for more complicated mixed integer programs for four such sets we give a complete description by valid inequalities and or an integral extended formulation and we also indicate what constraints can be added without destroying integrality we apply these results to provide tight formulations for certain piecewise linear convex objective integer programs and in a companion paper we exploit them to provide polyhedral descriptions and computationally effective mixed integer programming formulations for discrete lot sizing problems

an efficient trajectory method for probabilistic production inventory distribution problems we consider a supply chain operating in an uncertain environment the customers demand is characterized by a discrete probability distribution a probabilistic programming approach is adopted for constructing an inventory production distribution plan over a multiperiod planning horizon the plan does not allow the backlogging of the unsatisfied demand and minimizes the costs of the supply chain while enabling it to reach a prescribed nonstockout service level it is a strategic plan that hedges against undesirable outcomes and that can be adjusted to account for possible favorable realizations of uncertain quantities a modular integrated and computationally tractable method is proposed for the solution of the associated stochastic mixed integer optimization problems containing joint probabilistic constraints with dependent right hand side variables the concept of p efficiency is used to construct a finite number of demand trajectories which in turn are employed to solve problems with joint probabilistic constraints we complement this idea by designing a preordered set based preprocessing algorithm that selects a subset of promising p efficient demand trajectories finally to solve the resulting disjunctive mixed integer programming problem we implement a special column generation algorithm that limits the risk of congestion in the resources of the supply chain the methodology is validated on an industrial problem faced by a large chemical supply chain and turns out to be very efficient it finds a solution with a minimal integrality gap and provides substantial cost savings

types and unitary representations of reductive p adic groups we prove that for every bushnell kutzko type that satisfies a certain rigidity assumption the equivalence of categories between the corresponding bernstein component and the category of modules for the hecke algebra of the type induces a bijection between irreducible unitary representations in the two categories moreover we show that every irreducible smooth g representation contains a rigid type this is a generalization of the unitarity criterion of barbasch and moy for representations with iwahori fixed vectors

depth zero supercuspidal l packets for inner forms of gsp4 abstract we show that for any tame regular discrete series parameter of g s p 4 or its inner form g u 2 d the l packet attached by the local langlands conjecture gan and takeda 2011 14 gan and tantono submitted for publication 15 agrees with the l packet of depth zero supercuspidal representations constructed by debacker and reeder 2009 12

cuspidal ell modular representations of p adic classical groups for a classical group over a non archimedean local field of odd residual characteristic p we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p as representations induced from a cuspidal type we also give a fundamental step towards the classification of cuspidal representations identifying when certain cuspidal types induce to equivalent representations this result is new even in the case of complex representations finally we prove that the representations induced from more general types are quasi projective a crucial tool for extending the results here to arbitrary irreducible representations

nonlinear second order elliptic equations v the dirichlet problem for weingarten hypersurfaces on etudie le probleme de dirichlet pour une fonction u dans un domaine borne de r n a frontiere lisse strictement convexe en un point x de les courbures principales k k 1 k n du graphe x u x satisfont une relation f k 1 k n x 0 ou est une fonction positive lisse donnee sur de plus u doit satisfaire la condition aux limites de dirichlet u 0 sur sous certaines conditions on demontre qu il existe une solution u unique admissible lisse dans

singular sets for curvature equation of order k abstract we consider the removability of singular sets for the curvature equations of the form h k u which is determined by the kth elementary symmetric function in an n dimensional domain we prove that for 1 k n 1 and a compact set k whose n k dimensional hausdorff measure is zero any generalized solution to the curvature equation on k is always extendable to a generalized solution on the whole domain

spectral correspondences for affine hecke algebras we introduce the notion of spectral transfer morphisms between normalized affine hecke algebras and show that such morphisms induce spectral measure preserving correspondences on the level of the tempered spectra of the affine hecke algebras involved we define a partial ordering on the set of isomorphism classes of normalized affine hecke algebras which plays an important role for the langlands parameters of lusztig s unipotent representations

hecke algebras of classical groups over p adic fields and supercuspidal representations let k be a p adic field with involution 0 and let k 0 be its fixed subfield of k let v be a finite dimensional vector space defined over k equipped with e hermitian form v k 0 is large

hecke algebras and harmonic analysis on p adic groups we compute plancherel measures and formal degrees for unipotent representations of p adic groups using hecke algebra isomorphisms the results verify special cases of the conjectural uniformity of formal degrees in an l packet

extended deligne lusztig varieties for general and special linear groups abstract we give a generalisation of deligne lusztig varieties for general and special linear groups over finite quotients of the ring of integers in a non archimedean local field previously a generalisation was given by lusztig by attaching certain varieties to unramified maximal tori inside borel subgroups in this paper we associate a family of so called extended deligne lusztig varieties to all tamely ramified maximal tori of the group moreover we analyse the structure of various generalised deligne lusztig varieties and show that the unramified varieties including a certain natural generalisation do not produce all the irreducible representations in general on the other hand we prove results which together with some computations of lusztig show that for sl 2 f q 2 with odd q the extended deligne lusztig varieties do indeed afford all the irreducible representations

homological algebra for affine hecke algebras abstract in this paper we study homological properties of modules over an affine hecke algebra h in particular we prove a comparison result for higher extensions of tempered modules when passing to the schwartz algebra s a certain topological completion of the affine hecke algebra the proof is self contained and based on a direct construction of a bounded contraction of certain standard resolutions of h modules this construction applies for all positive parameters of the affine hecke algebra this is an important feature since it is an ingredient to analyse how the irreducible discrete series representations of h arise in generic families over the parameter space of h for irreducible non simply laced affine hecke algebras this will enable us to give a complete classification of the discrete series characters for all positive parameters we will report on this application in a separate article

second order conic approximation for disassembly line design with joint probabilistic constraints a problem of profit oriented disassembly line design and balancing with possible partial disassembly and presence of hazardous parts is studied the objective is to design a production line providing a maximal revenue with balanced workload task times are assumed to be random variables with known normal probability distributions the cycle time constraints are to be jointly satisfied with at least a predetermined probability level an and or graph is used to model the precedence relationships among tasks several lower and upper bounding schemes are developed using second order cone programming and convex piecewise linear approximation to show the relevance and applicability of the proposed approach a set of instances from the literature are solved to optimality

a linear programming approach for linear programs with probabilistic constraints we study a class of mixed integer programs for solving linear programs with joint probabilistic constraints from random right hand side vectors with finite distributions we present greedy and dual heuristic algorithms that construct and solve a sequence of linear programs we provide optimality gaps for our heuristic solutions via the linear programming relaxation of the extended mixed integer formulation of luedtke et al 2010 13 as well as via lower bounds produced by their cutting plane method while we demonstrate through an extensive computational study the effectiveness and scalability of our heuristics we also prove that the theoretical worst case solution quality for these algorithms is arbitrarily far from optimal our computational study compares our heuristics against both the extended mixed integer programming formulation and the cutting plane method of luedtke et al 2010 13 our heuristics efficiently and consistently produce solutions with small optimality gaps while for larger instances the extended formulation becomes intractable and the optimality gaps from the cutting plane method increase to over 5

optimization of a continuous distillation process under random inflow rate abstract the paper deals with a continuous distillation process under stochastic rate of inflows collected in a feed tank the aim of analysis is to find a robust control of extracting feed from the tank over a certain time horizon such that without knowledge of future realizations of the inflow rate some level constraints in the feed tank will be met with high probability this approach relies on formulating and numerically treating probabilistic constraints the inflow rate is considered as a stochastic process for which two basically different model assumptions are made the first model assumes a gaussian process and thus reflects the superposition of many independent elementary inflows the second model treats maybe the simplest case of a single elementary inflow profile namely rectangular inflows with fixed rate and duration but stochastic starting time numerical results illustrating both assumptions are presented and advantages over the simple anticipation of nominal inflow profiles are highlighted

analytic r groups of affine hecke algebras we define analytic r groups for affine hecke algebras and prove the analog of the knapp stein dimension theorem as a corollary we prove that the commutant algebra of a unitary principal series representation is isomorphic to the complex group algebra of the r group twisted by a certain 2 cocycle gamma for classical hecke algebras we prove that gamma is always trivial

hessian measures iii abstract in this paper we continue previous investigations into the theory of hessian measures we extend our weak continuity result to the case of mixed k hessian measures associated with k tuples of k convex functions on domains in euclidean n space k 1 2 n applications are given to capacity quasicontinuity and the dirichlet problem with inhomogeneous terms continuous with respect to capacity or combinations of dirac measures

hecke algebras from groups acting on trees and hnn extensions abstract we study hecke algebras of groups acting on trees with respect to geometrically defined subgroups in particular we consider hecke algebras of groups of automorphisms of locally finite trees with respect to vertex and edge stabilizers and the stabilizer of an end relative to a vertex stabilizer assuming that the actions are sufficiently transitive we focus on identifying the structure of the resulting hecke algebras give explicit multiplication tables of the canonical generators and determine whether the hecke algebra has a universal c completion the paper unifies algebraic and analytic approaches by focusing on the common geometric thread the results have implications for the general theory of totally disconnected locally compact groups

schur algebras of reductive p adic groups i we give a link through the affine schur algebra between the representations of the p affine schur algebra of gl n over r and the smooth r representations of the p adic group gl n qp over any algebraically closed field r of characteristic not equal to p

the breuil mezard conjecture when l neq p let l and p be primes let f qp be a finite extension with absolute galois group gf let f be a finite field of characteristic l and let w gf gln f be a continuous representation let r be the universal framed deformation ring for if l d p then the breuil mezard conjecture as recently formulated by emerton and gee relates the mod l reduction of certain cycles in r to the mod l reduction of certain representations of gln of we state an analogue of the breuil mezard conjecture when l p and we prove it whenever l 2 using automorphy lifting theorems we give a local proof when l is quasibanal for f and is tamely ramified we also analyze the reduction modulo l of the types defined by schneider and zink

a branch reduce cut algorithm for the global optimization of probabilistically constrained linear programs we consider probabilistically constrained linear programs with general distributions for the uncertain parameters these problems involve non convex feasible sets we develop a branch and bound algorithm that searches for a global optimal solution to this problem by successively partitioning the non convex feasible region and by using bounds on the objective function to fathom inferior partition elements this basic algorithm is enhanced by domain reduction and cutting plane strategies to reduce the size of the partition elements and hence tighten bounds the proposed branch reduce cut algorithm exploits the monotonicity properties inherent in the problem and requires solving linear programming subproblems we provide convergence proofs for the algorithm some illustrative numerical results involving problems with discrete distributions are presented

generalized solutions of curvature equations abstract we introduce a notion of generalized solutions for the so called curvature equations it is an extension of the definition of generalized solutions of the gauss curvature equation and gives a new framework for the study of more general curvature equations we prove that if the curvature equation has a convex solution then the inhomogeneous term must be a borel measure we also discuss basic properties of generalized solutions among other things we show that our class of generalized solutions is wider than that of weak solutions

mixing mixed integer inequalities mixed integer rounding mir inequalities play a central role in the development of strong cutting planes for mixed integer programs in this paper we investigate how known mir inequalities can be combined in order to generate new strong valid inequalities given a mixed integer region s and a collection of valid base mixed integer inequalities we develop a procedure for generating new valid inequalities for s the starting point of our procedure is to consider the mir inequalities related with the base inequalities for any subset of these mir inequalities we generate two new inequalities by combining or mixing them we show that the new inequalities are strong in the sense that they fully describe the convex hull of a special mixed integer region associated with the base inequalities we discuss how the mixing procedure can be used to obtain new classes of strong valid inequalities for various mixed integer programming problems in particular we present examples for production planning capacitated facility location capacitated network design and multiple knapsack problems we also present preliminary computational results using the mixing procedure to tighten the formulation of some difficult integer programs finally we study some extensions of this mixing procedure

unitary equivalences for reductive p adic groups we establish a transfer of unitarity for a bernstein component of the category of smooth representations of a reductive p adic group to the associated hecke algebra in the framework of the theory of types whenever the hecke algebra is an affine hecke algebra with geometric parameters in the sense of lusztig possibly extended by a group of automorphisms of the root datum it is known that there is a large class of such examples detailed in the paper as a consequence we establish relations between the unitary duals of different groups in the spirit of endoscopy

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

multiplicites modulaires et representations de rm gl sb 2 mathbf z sb p et de rm gal overline mathbf q sb p mathbf q sb p en ell p appendice par guy henniart sur l unicite des types pour rm gl sb 2

acyclicity of schneider and stuhler s coefficient systems another approach in the level 0 case let f be a non archimedean local field and g be the locally profinite group gl n f n 1 we denote by x the bruhat tits building of g for any smooth complex representation v of g and for any level n 1 schneider and stuhler have constructed a coefficient system c c v n on the simplicial complex x they proved that if v is generated by its fixed vectors under the principal congruence subgroup of level n then the augmented complex c or x c v of oriented chains of x with coefficients in c is a resolution of v in the category of smooth complex representations of g in this paper we give another proof of this result in the level 0 case and assuming moreover that v is generated by its fixed vectors under an iwahori subgroup i of g here level 0 refers to bushnell and kutzko s terminology that is to the case n 1 0 our approach is different we strongly use the fact that the trivial character of i is a type in the sense of bushnell and kutzko

theorie de lubin tate non abelienne ell entiere resume for two primes 6 p we investigate the z cohomology of the lubin tate towers of a p adic field we prove that it realizes some version of langlands and jacquet langlands correspondences for flat families of irreducible supercuspidal representations parametrized by a z algebra r in a way compatible with extension of scalars applied to r f this gives a cohomological realization of the langlands vigneras correspondence for supercuspidals and a new proof of its existence applied to complete local algebras this provides bijections between deformations of matching f representations besides we also get a virtual realization of both the semi simple langlands vigneras correspondence and the modular langlands jacquet transfer for all representations by using the cohomology complex and working in a suitable grothendieck group

construction of tame supercuspidal representations the notion of depth is defined by moy prasad mp2 the notion of a generic character will be defined in 9 when g gln or g is the multiplicative group of a central division algebra of dimension n with n p 1 our generic characters are just the generic characters in my where the definition is due to kutzko moreover in these cases our construction literally specializes to howe s construction as formulated in my and it is known that the construction yields all supercuspidal representations my hm notice that the initial datum in our construction consists of very simple objects linear characters and supercuspidal representations of depth zero the latter are well understood by the work of moy prasad and morris see 3 by the work of howe irreducible supercuspidal representations of gln f with n p 1 are parametrized by certain characters of e as e varies through

depth zero base change for ramified u 2 1 we give an explicit description of l packets and quadratic base change for depth zero representations of ramified unitary groups in two and three variables we show that this base change lifting is compatible with a certain lifting of families of representations of finite groups we conjecture that such a compatibility is valid in much greater generality

lifting of generic depth zero representations of classical groups abstract we describe how generic depth zero supercuspidal representations of classical groups lift to a general linear group the main tool is a computation of reducibility points of certain parabolically induced representations

iis branch and cut for joint chance constrained stochastic programs and application to optimal vaccine allocation we present a new method for solving stochastic programs with joint chance constraints with random technology matrices and discretely distributed random data the problem can be reformulated as a large scale mixed 0 1 integer program we derive a new class of optimality cuts called iis cuts and apply them to our problem the cuts are based on irreducibly infeasible subsystems iis of an lp defined by requiring that all scenarios be satisfied we propose a method for improving the upper bound of the problem when no cut can be found we derive and implement a branch and cut algorithm based on iis cuts and refer to this algorithm as the iis branch and cut algorithm we report on computational results with several test instances from optimal vaccine allocation the computational results are promising as the iis branch and cut algorithm gives better results than a state of the art commercial solver on one class of problems

the mixed vertex packing problem we study a generalization of the vertex packing problem having both binary and bounded continuous variables called the mixed vertex packing problem mvpp the well known vertex packing model arises as a subproblem or relaxation of many 0 1 integer problems whereas the mixed vertex packing model arises as a natural counterpart of vertex packing in the context of mixed 0 1 integer programming we describe strong valid inequalities for the convex hull of solutions to the mvpp and separation algorithms for these inequalities we give a summary of computational results with a branch and cut algorithm for solving the mvpp and using it to solve general mixed integer problems

pro p iwahori hecke algebra and supersingular representations the motivation of this paper is the search for a langlands correspondence modulo p we show that the pro p iwahori hecke ring h 1 of a split reductive p adic group g over a local field f of finite residue field fq with q elements admits an iwahori matsumoto presentation and a bernstein z basis and we determine its centre we prove that the ring h 1 is finitely generated as a module over its centre these results are proved in 12 only for the iwahori hecke ring let p be the prime number dividing q and let k be an algebraically closed field of characteristic p a character from the centre of h 1 to k which is as null as possible will be called null the simple h k modules with a null central character are called supersingular when g gl n we show that each simple h k module of dimension n containing a character of the affine subring h aff is supersingular the proof uses the minimal expressions of haines generalized to h 1 and that the number of such modules is equal to the number of irreducible k representations of the weil group wf of dimension n when the action of an uniformizer pf in the hecke algebra side and of the determinant of a frobenius frf in the galois side are fixed i e the number nn q of unitary irreducible polynomials in fq x of degree n one knows that the converse is true by explicit computations when n 2 11 and when n 3 rachel ollivier

removable singularities for fully nonlinear elliptic equations we obtain a removability result for the fully nonlinear uniformly elliptic equations f d 2 u f u 0 the main theorem states that every solution to the equation in a punctured ball without any restrictions on the behaviour near the centre of the ball is extendable to the solution in the entire ball provided the function f satisfies certain sharp conditions depending on f previously such results were known for linear and quasilinear operators f in comparison with the semi or quasilinear theory the techniques for the fully nonlinear equations are new and based on the use of the viscosity notion of generalised solution rather than the distributional or the weak solutions

resolutions of tempered representations of reductive p adic groups let g be a reductive group over a non archimedean local eld and let s g be its schwartz algebra we compare ext groups of tempered g representations in several module categories smooth g representations algebraic s g modules bornological s g modules and an exact category of s g modules on lf spaces which contains all admissible s g modules we simplify the proofs of known comparison theorems for these ext groups due to meyer and schneider zink our method is based on the bruhat tits building of g and on analytic properties of the schneider stuhler resolutions

an integer programming approach for linear programs with probabilistic constraints linear programs with joint probabilistic constraints pclp are difficult to solve because the feasible region is not convex we consider a special case of pclp in which only the right hand side is random and this random vector has a finite distribution we give a mixed integer programming formulation for this special case and study the relaxation corresponding to a single row of the probabilistic constraint we obtain two strengthened formulations as a byproduct of this analysis we obtain new results for the previously studied mixing set subject to an additional knapsack inequality we present computational results which indicate that by using our strengthened formulations instances that are considerably larger than have been considered before can be solved to optimality

semisimple types for p adic classical groups we construct for any symplectic unitary or special orthogonal group over a locally compact nonarchimedean local field of odd residual characteristic a type for each bernstein component of the category of smooth representations using bushnell kutzko s theory of covers moreover for a component corresponding to a cuspidal representation of a maximal levi subgroup we prove that the hecke algebra is either abelian or a generic hecke algebra on an infinite dihedral group with parameters which are at least in principle computable via results of lusztig in an appendix we make a correction to the proof of a result of the second author that every irreducible cuspidal representation of a classical group as considered here is irreducibly compactly induced from a type

a sample approximation approach for optimization with probabilistic constraints we study approximations of optimization problems with probabilistic constraints in which the original distribution of the underlying random vector is replaced with an empirical distribution obtained from a random sample we show that such a sample approximation problem with a risk level larger than the required risk level will yield a lower bound to the true optimal value with probability approaching one exponentially fast this leads to an a priori estimate of the sample size required to have high confidence that the sample approximation will yield a lower bound we then provide conditions under which solving a sample approximation problem with a risk level smaller than the required risk level will yield feasible solutions to the original problem with high probability once again we obtain a priori estimates on the sample size required to obtain high confidence that the sample approximation problem will yield a feasible solution to the original problem finally we present numerical illustrations of how these results can be used to obtain feasible solutions and optimality bounds for optimization problems with probabilistic constraints

an explicit matching theorem for level zero discrete series of unit groups of p adic simple algebras for a f a central simple algebra over a p adic local field the group of units a glm dd is a general linear group over a central division algebra dd f of index d the product n dm being fixed the abstract matching theorem amt implies the existence of bijective maps jl between the sets of discrete series representations of the groups a such that a character relation is preserved in this paper we construct maximal level zero extended type components for every level zero discrete series representation of a its maximal level zero extended type determines the discrete series representation uniquely without any twist ambiguities as for the usual types and conversely every level zero discrete series representation contains a maximal level zero extended type component which is unique up to conjugacy in order to determine how jl matches the extended types we find certain regular elliptic elements where the characters of and are the same and we compute the character values at these elements by using a version of shintani descent which we develop in appendix b surprisingly we find that amt also implies explicit shintani descent for irreducible characters of finite general linear groups which have cuspidal descent named author let f be a locally compact p adic field let dd be a central division algebra of index d over f and let a mm dd the algebra of all m m matrices with entries in dd then a is a central simple f algebra of reduced degree n dm and the group of units a of a is the group of f points of a connected reductive algebraic group defined over f the group a is separable totally disconnected and unimodular and the harmonic analysis of a as is well known is linked to numerous problems in arithmetic it is interesting and perhaps may be regarded as a version of the abstract matching theorem amt see 0 2 that the representation theory of a depends upon the parameters d m associated to a but not more specifically on the isomorphism class of a we follow the convention of writing dd for any central f division algebra of index d we also write dn for any one of the n isomorphism class representatives of central f division algebras of index n 1991 mathematics subject classification 22e50 1the work reported in this paper grew out of a research in pairs sojourn at the mathematisches institut oberwolfach the authors wish to express their appreciation to the institut for its support of their research as well as for an enjoyable stay at the institut

on mixing sets arising in chance constrained programming the mixing set with a knapsack constraint arises in deterministic equivalent of chance constrained programming problems with finite discrete distributions we first consider the case that the chance constrained program has equal probabilities for each scenario we study the resulting mixing set with a cardinality constraint and propose facet defining inequalities that subsume known explicit inequalities for this set we extend these inequalities to obtain valid inequalities for the mixing set with a knapsack constraint in addition we propose a compact extended reformulation with polynomial number of variables and constraints that characterizes a linear programming equivalent of a single chance constraint with equal scenario probabilities we introduce a blending procedure to find valid inequalities for intersection of multiple mixing sets we propose a polynomial size extended formulation for the intersection of multiple mixing sets with a knapsack constraint that is stronger than the original mixing formulation we also give a compact extended linear program for the intersection of multiple mixing sets and a cardinality constraint for a special case we illustrate the effectiveness of the proposed inequalities in our computational experiments with probabilistic lot sizing problems

a satake isomorphism for representations modulo p of reductive groups over local fields let f be a local field with finite residue field of characteristic p let g be a connected reductive group over f and b a minimal parabolic subgroup of g with levi decomposition b zu let k be a special parabolic subgroup of g in good position relative to z u fix an absolutely irreducible smooth representation of k on a vector space v over some field c of characteristic p writing h g k v for the intertwining hecke algebra of v in g we define a natural algebra homomorphism from h g k v to h z z k v u k we show it is injective and identify its image we thus generalize work of f herzig who assumed f of characteristic 0 g unramified and k hyperspecial and took for c an algebraic closure of the prime field fp we show that in the general case h g k v need not be commutative that is in contrast with the cases herzig considers and with the more classical situation where v is trivial and the field of coefficients is the field of complex numbers

on crystabelline deformation rings of mathrm gal overline mathbb q _p mathbb q _p with an appendix by jack shotton we prove that certain crystabelline deformation rings of two dimensional residual representations of mathrm gal overline mathbb q p mathbb q p are cohen macaulay as a consequence this allows to improve kisin s r 1 p mathbb t 1 p theorem to an r mathbb t theorem

the supercuspidal representations of p adic classical groups let g be a unitary symplectic or special orthogonal group over a locally compact non archimedean local field of odd residual characteristic we construct many new supercuspidal representations of g and bushnell kutzko types for these representations moreover we prove that every irreducible supercuspidal representation of g arises from our constructions

isolated singularities for some types of curvature equations abstract we consider the removability of isolated singularities for the curvature equations of the form h k u 0 which is determined by the k th elementary symmetric function in an n dimensional domain we prove that for 1 k n 1 isolated singularities of any viscosity solutions to the curvature equations are always removable provided the solution can be extended continuously at the singularities we also consider the class of generalized solutions and prove the removability of isolated singularities

discrete series characters for affine hecke algebras and their formal degrees we introduce the generic central character of an irreducible discrete series representation of an affine hecke algebra using this invariant we give a new classification of the irreducible discrete series characters for all abstract affine hecke algebras except for the types e n 1 n 6 7 8 with arbitrary positive parameters and we prove an explicit product formula for their formal degrees in all cases

resolutions for representations of reductive p adic groups via their buildings schneider stuhler and vigneras have used cosheaves on the affine bruhat tits building to construct natural projective resolutions of finite type for admissible representations of reductive p adic groups in characteristic not equal to p we use a system of idempotent endomorphisms of a representation with certain properties to construct a cosheaf and a sheaf on the building and to establish that these are acyclic and compute homology and cohomology with these coefficients this implies bernstein s result that certain subcategories of the category of representations are serre subcategories furthermore we also get results for convex subcomplexes of the building following work of korman this leads to trace formulas for admissible representations

hecke algebra with respect to the pro p radical of a maximal compact open subgroup for gl n f and its inner forms abstract let g be a direct product of inner forms of general linear groups over non archimedean locally compact fields of residue characteristic p and let k 1 be the pro p radical of a maximal compact open subgroup of g in this paper we describe the intertwining hecke algebra h g k 1 that is the convolution z algebra of functions from g to z that are bi invariant for k 1 and whose supports are a finite union of k 1 double cosets we produce a presentation by generators and relations of this algebra finally we prove that the level 0 subcategory of the category of smooth representations of g over a unitary commutative ring r such that p r is equivalent to the category of modules over h g k 1 z r

theorie de lubin tate non abelienne et representations elliptiques non abelian lubin tate theory studies the cohomology of some moduli spaces for p divisible groups the broadest definition of which is due to rapoport zink aiming both at providing explicit realizations of local langlands functoriality and at studying bad reduction of shimura varieties in this paper we consider the most famous examples the so called drinfeld and lubin tate towers in the lubin tate case harris and taylor proved that the supercuspidal part of the cohomology realizes both the local langlands and jacquet langlands correspondences as conjectured by carayol recently boyer computed the remaining part of the cohomology and exhibited two defects first the representations of gl d which appear are of a very particular and restrictive form second the langlands correspondence is not realized anymore in this paper we study the cohomology complex in a suitable equivariant derived category and show how it encodes langlands correspondence for elliptic representations then we transfer this result to the drinfeld tower via an enhancement of a theorem of faltings due to fargues we deduce that deligne s weight monodromy conjecture is true for varieties uniformized by drinfeld s coverings of his symmetric spaces this completes the computation of local l factors of some unitary shimura varieties

probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra we consider stochastic programming problems with probabilistic constraints involving random variables with discrete distributions they can be reformulated as large scale mixed integer programming problems with knapsack constraints using specific properties of stochastic programming problems and bounds on the probability of the union of events we develop new valid inequalities for these mixed integer programming problems we also develop methods for lifting these inequalities these procedures are used in a general iterative algorithm for solving probabilistically constrained problems the results are illustrated with a numerical example

on the hecke algebra of a type for unramified p adic unitary groups abstract let f be a non archimedean local field of odd residue characteristic equipped with a galois involution with fixed field f 0 and let g be a symplectic group over f or an unramified unitary group over f 0 for a simple type j p p in g which is a g cover associated to a certain simple stratum we show that the corresponding hecke algebra h g p is generic

hessian measures ii in our previous paper on this topic we introduced the notion of k hessian measure associated with a continuous k convex function in a domain q in euclidean n space k 1 n and proved a weak continuity result with respect to local uniform convergence in this paper we consider k convex functions not necessarily continuous and prove the weak continuity of the associated k hessian measure with respect to convergence in measure the proof depends upon local integral estimates for the gradients of k convex functions

compactness theorems for differential forms we prove compactness properties of various sets of differential forms with bounds on their exterior derivatives this gives simple proofs of the federer fleming result on normal currents and of compensated compactness lemmas

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

some examples of square integrable representations of semisimple p adic groups we construct irreducible representations of the hecke algebra of an affine weyl group analogous to kilmoyer s reflection representation corresponding to finite weyl groups and we show that in many cases they correspond to a square integrable representation of a simple p adic group

pro p iwahori hecke ring and supersingular representations the motivation of this paper is the search for a langlands correspondence modulo p we show that the pro p iwahori hecke ring open image in new window of a split reductive p adic group g over a local field f of finite residue field fq with q elements admits an iwahori matsumoto presentation and a bernstein z basis and we determine its centre we prove that the ring open image in new window is finitely generated as a module over its centre these results are proved in 11 only for the iwahori hecke ring let p be the prime number dividing q and let k be an algebraically closed field of characteristic p a character from the centre of open image in new window to k which is as null as possible will be called null the simple open image in new window modules with a null central character are called supersingular when g gl n we show that each simple open image in new window module of dimension n containing a character of the affine subring open image in new window is supersingular using the minimal expressions of haines generalized to open image in new window and that the number of such modules is equal to the number of irreducible k representations of the weil group wf of dimension n when the action of an uniformizer pf in the hecke algebra side and of the determinant of a frobenius frf in the galois side are fixed i e the number nn q of unitary irreducible polynomials in fq x of degree n one knows that the converse is true by explicit computations when n 2 10 and when n 3 rachel ollivier