on certain functions for deformations of knot group representations we study the twisted knot module for the universal deformation of an sl2 representation of a knot group and introduce an associated l function which may be seen as an analogue of the algebraic p adic lfunction associated to the selmer module for the universal deformation of a galois representation we then verify affirmatively mazur s problem on the order of a zero of the l function by some examples for 2 bridge knots

eigenvarieties for reductive groups we develop the theory of overconvergent cohomology introduced by g stevens and we use it to give a construction of eigenvarieties associated to any reductive group g over q such that g r has discrete series we prove that the so called eigenvarieties are equidimensional and generically at over the weight space

on the main conjecture for cm fields the aim of this work is to prove a divisibility relation toward the main conjecture for cm fields our main tool is the study of congruences between an eisenstein series and cusp forms on the unitary group gu 2 1 we introduce an eisenstein ideal in the nearly ordinary universal hecke algebra for gu 2 1 and show that it divides the characteristic ideal of the cm iwasawa module

higher coherent cohomology and p adic modular forms of singular weights we investigate the p adic properties of higher coherent cohomology of automorphic vector bundles of singular weights on siegel threefolds

hat g local systems on smooth projective curves are potentially automorphic dfg grants fg 1920 and spp 1489 erc grant 290766 aamot nsf grant dms 1404769 nsf grant dms 1161671 humboldt research award clay mathematics institute erc grant no 714405 gmlp

module de congruences pour gl 2 d un corps imaginaire quadratique et theorie d iwasawa d un corps cm biquadratique

on the images of modular and geometric three dimensional galois representations we study compatible families of three dimensional galois representations constructed in the etale cohomology of a smooth projective variety we prove a theorem asserting that the residual images will be generically large if certain easy to check conditions are satisfied we only consider representations with coefficients in an imaginary quadratic field for primes inert in this field the residual representations when irreducible are unitary we apply our result to an example constructed by van geemen and top obtaining a family of special linear groups and one of special unitary groups as galois groups over inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i we also consider the case of cohomological modular forms for a congruence subgroup of sl inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i assuming clozel s conjecture stating that a geometric family of three dimensional galois representations can be attached to them we verify for three examples the conditions guaranteeing generically large images and explicitly bound the finite set of primes with non maximal image we also discuss what intrinsic conditions a modular form should verify to guarantee that the images of the attached galois representations will be generically large

the fontaine mazur conjecture for gl _2 introduction 641 1 breuil mezard conjecture and the p adic local langlands 644 1 1 the breuil mezard conjecture 644 1 2 review of colmez s functor 647 1 3 hilbert samuel multiplicities 650 1 4 representations and pseudo representations 653 1 5 gl2 qp representations mod p 657 1 6 local patching and multiplicities 661 1 7 from pseudo representations to representations 669 2 modularity via the breuil mezard conjecture 675 2 1 quaternionic forms 675 2 2 global patching and multiplicities 677 2 3 the breuil mezard conjecture 686 addendum to ki 1 687 references 689

a faster capacity scaling algorithm for minimum cost submodular flow we describe an o n exp 4 h min log u n exp 2 log n capacity scaling algorithm for the minimum cost submodular flow problem our algorithm modifies and extends the edmonds karp capacity scaling algorithm for minimum cost flow to solve the minimum cost submodular flow problem the modification entails scaling a relaxation parameter delta capacities are relaxed by attaching a complete directed graph with uniform arc capacity delta in each scaling phase we then modify a feasible submodular flow by relaxing the submodular constraints so that complementary slackness is satisfied this creates discrepancies between the boundary of the flow and the base polytope of a relaxed submodular function to reduce these discrepancies we use a variant of the successive shortest path algorithm that augments flow along min cost paths of residual capacity at least delta the shortest augmenting path subroutine we use is a variant of dijkstra s algorithm modified to handle exchange capacity arcs efficiently the result is a weakly polynomial time algorithm whose running time is better than any existing submodular flow algorithm when u is small and c is big we also show how to use max mean cuts to make the algorithm strongly polynomial the resulting algorithm is the first capacity scaling algorithm to match the current best strongly polynomial bound for submodular flow

erratum to mass equidistribution for automorphic forms of cohomological type on gl_ 2 corollary 3 of 4 is not known unconditionally as cohomological automorphic forms on gl2 over an imaginary quadratic field are not known to satisfy the ramanujan conjecture we shall briefly describe the reason for this and discuss what information theorem 1 of 4 does give in the case of imaginary quadratic fields let k be an imaginary quadratic field with nontrivial automorphism c and let be a cuspidal automorphic representation of gl2 ak with unitary central character suppose that and that has langlands parameter wc c gl2 c given by z diag z1 k z1 k for some integer k 2 i e so that is any cohomological representation up to twist it is then known see theorem 1 1 of 1 that for any one may associate a continuous irreducible representation gal k k gl2 q to such that the characteristic polynomial of frobv agrees with the hecke polynomial of v at all places v which do not divide and at which k q and are unramified however because is constructed via an adic limiting process it is not known to arise from a motive and so is not known to be pure to construct one first makes a theta lift from to a holomorphic limit of discrete series representation on sp4 q as in 3 weissauer 6 has proven that if is a holomorphic discrete series representation of sp4 q which is not a cap representation then one may associate a galois representation to it which is pure and locally compatible with at all unramified places so that satisfies ramanujan wherever it is unramified these results are not known for the limit of discrete series representation and to associate a galois representation to it one must apply techniques of taylor 5 which are similar to those used by deligne and serre to associate galois representations to classical weight 1 modular forms these involve multiplying a holomorphic form in by a well understood regular holomorphic form of large weight applying the results of weissauer and recovering from these products by an adic limiting process any archimedean information about the frobenius eigenvalues of is lost during this and neither does one know that arises from a motive as a result the algebraic information we obtain about is insufficient to deduce ramanujan for it we may still draw interesting conclusions from theorem 1 of 4 in the imaginary quadratic case cohomological forms on gl2 k which are base changes from q will satisfy ramanujan and so theorem 1 establishes their equidistribution as their weight becomes large moreover the experimental results of 2 suggest that all

on a class of rational matrix differential equations arising in stochastic control we prove a monotonicity and a comparison theorem for the solutions of a rational matrix differential equation appearing in stochastic control and derive existence and convergence results for the solutions of this differential equation moreover in the time invariant case we present conditions ensuring that the corresponding algebraic matrix equation has a stabilizing solution

strata hasse invariants hecke algebras and galois representations we construct group theoretical generalizations of the hasse invariant on strata closures of the stacks mathop g hbox mathtt zip nolimits mu restricting to zip data of hodge type we obtain a group theoretical hasse invariant on every ekedahl oort stratum closure of a general hodge type shimura variety a key tool is the construction of a stack of zip flags mathop g hbox mathtt zipflag nolimits mu fibered in flag varieties over mathop g hbox mathtt zip nolimits mu it provides a simultaneous generalization of the classical case homogeneous complex manifolds studied by griffiths schmid and the flag space for siegel varieties studied by ekedahl van der geer four applications are obtained 1 pseudo representations are attached to the coherent cohomology of hodge type shimura varieties modulo a prime power 2 galois representations are associated to many automorphic representations with non degenerate limit of discrete series archimedean component 3 it is shown that all ekedahl oort strata in the minimal compactification of a hodge type shimura variety are affine thereby proving a conjecture of oort 4 part of serre s letter to tate on mod p modular forms is generalized to general hodge type shimura varieties

the iwasawa main conjectures for gl2 we prove the one two and three variable iwasawa greenberg main conjectures for a large class of modular forms that are ordinary with respect to an odd prime p the method of proof involves an analysis of an eisenstein ideal for ordinary hida families for gu 2 2