92 research outputs found
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A relation between Mirkovic-Vilonen cycles and modules over preprojective algebra of Dynkin quiver of type ADE
No full textThe irreducible components of the variety of all modules over the preprojective algebra and MV cycles both index bases of the universal enveloping algebra of the positive part of a semisimple Lie algebra canonically. To relate these two objects Baumann and Kamnitzer associate a cycle in the affine Grassmannian to a given module. It is conjectured that the ring of functions of the T-fixed point subscheme of the associated cycle is isomorphic to the cohomology ring of the quiver Grassmannian of the module. I give a proof of part of this conjecture. The relation between this conjecture and the reduceness conjecture is explained at the end.MathematicsDoctor of Philosophy (Ph.D.
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SEMI-INFINITE FLAGS AND ZASTAVA SPACES
No full textABSTRACT SEMI-INFINITE FLAGS AND ZASTAVA SPACES SEPTEMBER 2023 ANDREAS HAYASH, B.A., HAMPSHIRE COLLEGE M.S., UNIVERSITY OF MASSACHUSETTS AMHERST Ph.D, UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Ivan Mirković We give an interpretation of Dennis Gaitsgory’s semi-infinite intersection cohomol- ogy sheaf associated to a semisimple simply-connected algebraic group in terms of finite-dimensional geometry. Specifically, we construct machinery to build factoriza- tion spaces over the Ran space from factorization spaces over the configuration space, and show that under this procedure the compactified Zastava space is sent to the support of the semi-infinite intersection cohomology sheaf in the Beilinson-Drinfeld Grassmannian. We also construct a partial resolution of singularities of the compact- ified Zastava space and show that the Zastava version of the semi-infinite intersection cohomology sheaf is pulled back to the ordinary (perverse) intersection cohomology sheaf of the partial resolution. Lastly, we show that there is a monad acting on sheaves over the resolution whose category of modules embeds fully faithfully in sheaves on the affine Grassmannian.MathematicsDoctor of Philosophy (Ph.D.
Affine braid group actions on derived categories of springer resolutions
No full textAuthor Manuscript 14 May 2011In this paper we construct and study an action of the affine braid group associated to a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the Springer resolution of the nilpotent cone. In particular, we describe explicitly the action of the Artin braid group. This action is a "categorical version" of Kazhdan--Lusztig--Ginzburg's construction of the affine Hecke algebra, and is used in particular by the first author and Ivan Mirkovic in the course of the proof of Lusztig's conjectures on equivariant K-theory of Springer fibers
The affects of GDPR on companies: : a study about the impact of GDPR on the collection of personal data for target marketing and data mining.
No full textTitle: The affects of GDPR on companies: a study about the impact of GDPR on the collection of personal data for target marketing and data mining. Keywords: GDPR, target marketing, data mining Subject: Bachelor's thesis, International Marketing, 15hp. Author: Denise Loponen Mejia & Viktoria Mirkovic Problem: How has GDPR affected companies when collecting personal data for target marketing and data mining? Purpose: The purpose of this study is to clarify the affects that GDPR has had on companies and what alterations the companies have had to make since the enforcement of the regulation regarding target marketing and data mining. Method: In this study a deductive method has been applied. Primary data has been obtained through qualitative semi-structured interviews, which were transcribed and analyzed in order to find a conclusion. Conclusion: The conclusion of this study shows that GDPR has had an impact on companies regarding their collection of personal data. The companies have had to change the way they have handled this in comparison to before. Furthermore, implementation of new strategies in order to be able to identify customer groups and lawfully be able to use data mining has had to be established. Moreover, the study shows that companies have had to introduce changes in order to comply with the regulation, as well as the fact that the change has been successful. Titel: Påverkan av GDPR på företag: en studie om betydelsen av GDPR för insamling av personliga uppgifter till target marketing och data mining. Nyckelord: GDPR, target marketing, data mining. Ämne: Kandidatuppsats i företagsekonomi, inriktning internationell marknadsföring, 15 hp Författare: Denise Loponen Mejia & Viktoria Mirkovic Problemformulering: Hur har GDPR påverkat företag vid insamling av personlig data till target marketing och data mining? Syfte: Syftet med denna studie är att klargöra hur införandet av GDPR har påverkat företag och vilka ändringar de har varit tvungna till att införa vid insamling av personliga uppgifter till target marketing och data mining. Metod: I denna studie har en deduktiv metod tillämpats. Primärdata har nhämtats genom kvalitativa semi-strukturerade intervjuer, vilka sedan transkriberat och analyseras i syfte att finna ett svar på frågeställningen. Slutsats: Resultatet av denna studie påvisar att GDPR har haft en påverkan på hur företag hanterar insamling och hantering av personlig data. De har blivit tvungna till att förändra sättet de hanterar detta på. Även implementering av nya strategier för att kunna identifiera kundgrupper och lagligt använda data mining har krävts. Vidare visar resultatet att samtliga företag har fått införa förändringar för att efterfölja den nya regleringen, samt att den har varit framgångsrik.
Linear Koszul duality and Fourier transform for convolution algebras
No full textv1: 29 pages; v2: 41 pages, many details added; v3: 42 pages, minor modifications (final version, to appear in Doc. Math.)International audienceIn this paper we prove that the linear Koszul duality isomorphism for convolution algebras in K-homology defined in a previous paper and the Fourier transform isomorphism for convolution algebras in Borel-Moore homology are related by the Chern character. So, Koszul duality appears as a categorical upgrade of Fourier transform of constructible sheaves. This result explains the connection between the categorification of the Iwahori-Matsumoto involution for graded affine Hecke algebras (due to Evens and the first author) and for usual affine Hecke algebras (obtained in a previous paper)
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A CATEGORICAL FORMULATION OF ALGEBRAIC GEOMETRY
No full textWe construct a category, , of which the objects are pointed categories and the arrows are pointed correspondences. The notion of a ``spec datum" is introduced, as a certain relation between categories, of which one has been given a Grothendieck topology. A ``geometry" is interpreted as a sub-category of , and a formalism is given by which such a subcategory is to be associated to a spec datum, reflecting the standard construction of the category of schemes from the category of rings by affine charts.MathematicsDoctor of Philosophy (Ph.D.
Stability Conditions for Slodowy Slices and Real Variations of Stability
No full textThe paper provides new examples of an explicit submanifold in
Bridgeland stabilities space of a local Calabi-Yau. More precisely, let X be the standard resolution of a transversal slice to an adjoint nilpotent orbit of a simple Lie algebra over C. An action of the affine braid group on the derived category D[superscript b] (Coh(X)) and a collection of t-structures on this category permuted by the action have been constructed in [BR] and [BM] respectively. In this note we show that the t-structures come from points in a certain connected submanifold in the space of Bridgeland
stability conditions. The submanifold is a covering of a submanifold in the
dual space to the Grothendieck group, and the affine braid group acts by deck transformations. We also propose a new variant of definition of stabilities on a triangulated category, which we call a ”real variation of stability conditions” and discuss its relation to Bridgeland’s definition. The main theorem provides an illustration of such a relation. We state a conjecture by the second author and A. Okounkov on examples of this structure arising from symplectic resolutions of singularities and its relation to equivariant quantum cohomology. We verify this conjecture in our examples
Iwahori-Matsumoto involution and linear Koszul Duality
No full text29 pages, version finale, publié dans IMRNInternational audienceWe use linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras studied in previous papers of the authors, to give a geometric realization of the Iwahori--Matsumoto involution of affine Hecke algebras. More generally we prove that linear Koszul duality is compatible with convolution in a general context related to convolution algebras
Linear Koszul duality
No full textInternational audienceIn this paper we construct, for F_1 and F_2 subbundles of a vector bundle E, a ``Koszul duality'' equivalence between derived categories of \Gm-equivariant coherent (dg-)sheaves on the derived intersection of F_1 and F_2 inside E, and the corresponding derived intersection of orthogonals in the dual vector space. We also propose applications to Hecke algebras
Choice of surgical suture material used in oral cavity: Clinical study
No full textIntroduction. Historical data on closing and suturing of surgical wounds
describe a wide range of various suture materials. The choice of the surgical
catgut, i.e. type and diameter, depends on the localization, characteristics
and condition of the tissue to be treated. From the stand-point of
oral-surgical practice the following clinical parameters are of the
outstanding importance regarding the choice of suture material: accumulation
of soft deposits on the sutures, decubitus of the adjacent soft tissues and
dehiscence of the operative wound. Aim. The aim of this research was to
determine the correlation between different types of suture materials and
accumulation of soft deposits on the sutures, decubitus of the adjacent soft
tissues and dehiscence of the operative wound. Material and methods. Our
prospective clinical study included 150 patients distributed into three
groups of 50 subjects. The surgical procedure performed on each patient
involved resection (apicoectomy) of the tooth root end in the intercanine
sector of the upper jaw. The following suture materials were applied: BLACK
SILK 5-0, NYLON 5-0 and VICRYL 5-0. The effects of the selected sutures were
evaluated by using several parameters: accumulation of soft deposits, wound
dehiscence and decubitus of the adjacent soft tissues. The effects of the
applied sutures were recorded on days 2, 5 and 7 after the surgery.
Conclusion. The comparison of cited parameters of the investigated materials
after suture of oral cavity mucosa revealed that none of the used material
was ideal; however, a certain preference might be given to the synthetic
monofilament suture materials.</jats:p
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