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- Description:
- Let X,Y be algebraic varieties defined over the reals. Assume Y is smooth and X is Gorenstein. Suppose f:X -> Y is a flat R-morphism such that all the fibers have rational singularities. We show that the pushforward of any smooth, compactly supported measure on X has a continuous density...
- Keyword:
- Measures and Rational singularities
- Subject:
- Mathematics
- Creator:
- Andrew Reiser
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 11/24/2019
- Date Modified:
- 11/24/2019
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
-
- Description:
- We compare two different methods to compute the mod 2 homology of an infinite loop space. One method is to approximate the infinite loop functor using functor calculus. The other is to approximate the spectrum using an Adams resolution. We show that these two ways lead to isomorphic spectral sequences....
- Keyword:
- spectral sequences, Goodwillie calculus, Adams resolution, and power operations
- Subject:
- Mathematics
- Creator:
- Johan W T Konter
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 11/24/2019
- Date Modified:
- 11/24/2019
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
-
- Description:
- The moduli stack of bundles on a smooth complete curve over a field, is an immensely rich geometric object and is of central importance to the Geometric Langlands program. This thesis represents a contribution towards a motivic, in the sense of Voevodsky and Morel-Voevodsky, understanding of this stack. Following the...
- Keyword:
- Space of rational maps, Ran space, Motivic homotopy theory, Motives, and Geometric Langlands
- Subject:
- Mathematics
- Creator:
- Elden Elmanto
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 11/19/2019
- Date Modified:
- 11/19/2019
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
-
- Description:
- In this work we explore a connection between some high dimensional asymptotic problems and random matrix theory. In the first part, we establish a link between the Wishart ensemble and random critical points of holomorphic sections over complex projective space and use this to establish asymptotics on the average number...
- Keyword:
- High Dimensional, Complex Geometry, Differential Equations, and Probability Theory
- Subject:
- Mathematics
- Creator:
- Xavier Eduardo Garcia
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 11/19/2019
- Date Modified:
- 11/19/2019
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
-
- Description:
- This thesis is naturally split into two parts. In the first part, we develop the theory of multi- linear algebra for Tate objects over exact categories endowed with an exact tensor product. We study all possible choices of tensor product and we give a geometric interpretation of the results. In...
- Keyword:
- Tate objects, tensor product, central extension, and determinant
- Subject:
- Mathematics
- Creator:
- Aron Alexandre Heleodoro
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 04/15/2019
- Date Modified:
- 04/15/2019
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
-
- Description:
- In this thesis, we study arithmetic phenomena exhibited by polynomial dynamical systems on the projective line. Specifically, given a number field $K$, we are interested in the arithmetic of orbits of points $\alpha\in K$ under polynomials $\phi\in K[z]$. Given such a polynomial $\phi$ of degree $d\ge2$, we prove a lower...
- Keyword:
- Mathematics
- Subject:
- Mathematics
- Creator:
- Nicole Romain Looper
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 04/09/2019
- Date Modified:
- 04/09/2019
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
-
- Description:
- In this paper, we show almost-Gelfand property of connected symmetric pairs (G, H) over finite fields of large characteristics by showing almost-sigma-invariant property of double coset H\G/H where sigma is the associated anti-involution combining with epsilon-version of Gelfand's trick
- Keyword:
- symmetric pair, representation theory, and Gelfand pair
- Subject:
- Mathematics
- Creator:
- Nan Shi
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 04/01/2019
- Date Modified:
- 04/01/2019
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
-
- Description:
- The holomorphic sigma-model is a field theory that exists in any complex dimension that describes the moduli space of holomorphic maps from one complex manifold to another. We introduce the general notion of a holomorphic field theory, which is one that is sensitive to the underlying complex structure of the...
- Keyword:
- Factorization algebras, Renormalization, Batalin-Vilkovisky, and Quantum field theory
- Subject:
- Mathematics
- Creator:
- Brian R Williams
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 04/01/2019
- Date Modified:
- 04/01/2019
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
-
- Description:
- homotopy theory studies a parametrization of stable homotopy theory in terms of algebraic objects called formal groups. Transchromatic homotopy theory is specifically concerned with the behavior of spaces and cohomology theories as these formal groups change in height. We pursue a central transchromatic object, the K(n − 1)- localization of...
- Keyword:
- chromatic homotopy theory, formal groups, Morava E-theory, Bousfield localization, algebraic topology, and structured ring spectra
- Subject:
- Mathematics
- Creator:
- Paul Behrents VanKoughnett
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 04/01/2019
- Date Modified:
- 04/01/2019
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
-
- Description:
- We prove a uniform scalar curvature bound for solutions of the conical Kahler-Ricci flow when the twisted canonical bundle is semiample and the cone divisor is obtained from the associated Iitaka-Kodaira fibration. In the course of the proof we establish uniform bounds for the potential of the metric and its...
- Keyword:
- Geometric Flows, Kahler-Ricci Flow, and Conical Kahler Metrics
- Subject:
- Mathematics
- Creator:
- Gregory Edwards
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 03/07/2019
- Date Modified:
- 03/07/2019
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
-
- Description:
- In fish, caudally propagating waves of neural activity produce muscle bending moments. These moments, coupled with forces due to the body's elastic properties and forces due to fluid-body interactions, determine the deformation kinematics for swimming. Fully resolved simulations of neurally-activated swimming can be used to decode activation patterns underlying observed...
- Keyword:
- biomechanics, fluid structure interaction, locomotion, neuromechanics, neuromechanical phase lag, and immersed boundary method
- Subject:
- Mathematics
- Creator:
- Namrata Kartik Patel
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 01/09/2019
- Date Modified:
- 01/29/2019
- Date Created:
- 2017-01-01
- Resource Type:
- Dissertation
-
- Description:
- In this thesis we study minimal measures for Lagrangian systems on compact manifolds. This thesis consists of three parts which are closely related. The first part is Chapter 3 and Chapter 4. In Chapter 3 and 4, we consider geodesic flows on compact surfaces with higher genus. We show that...
- Keyword:
- Minimal Measures
- Subject:
- Mathematics
- Creator:
- Fang Wang
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 10/02/2018
- Date Modified:
- 10/02/2018
- Date Created:
- 2008-08-22
- Resource Type:
- Dissertation
-
- Description:
- The Witten Laplacian corresponding to a Morse function on the circle is studied using methods of complex WKB and resurgent analysis. It is shown that under certain assumptions the low-lying eigenvalues of the Witten Laplacian are resurgent.
- Keyword:
- Mathematics
- Subject:
- Mathematics
- Creator:
- Alexander Getmaneko
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 09/14/2018
- Date Modified:
- 09/14/2018
- Date Created:
- 2008-08-11
- Resource Type:
- Dissertation
-
- Description:
- This paper covers three main topics. The first is addressing the question of interpolating between disparate index theorems on noncommutative two-tori. The second is to compute Hochschild cohomology for quantum special linear and special unitary groups. The third is producing an orthonormal basis for the vector space of matrix corepresentations...
- Keyword:
- Mathematics
- Subject:
- Mathematics
- Creator:
- Gary Clark Alexander
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 09/10/2018
- Date Modified:
- 09/10/2018
- Date Created:
- 2008-05-09
- Resource Type:
- Dissertation
-
- Description:
- The homotopy groups of bo^tmf are shown to be isomorphic to the homotopy groups of a wedge of suspensions of spectra related to integral Brown-Gitler spectra. We will then restate Mahowald's proof of the topological splitting of bo^bo and subsequently apply similar techniques to construct a map that realizing the...
- Keyword:
- integral Brown Gitler spectra, tmf, and Tate spectrum
- Subject:
- Mathematics
- Creator:
- Scott MIchael Bailey
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 09/07/2018
- Date Modified:
- 09/07/2018
- Date Created:
- 2008-05-09
- Resource Type:
- Dissertation
-
- Description:
- This dissertation addresses the structure of the group of interval exchange transformations. The two primary topics considered are: a) the classification of interval exchange actions for certain groups; and b) properties of the interval exchange group which are reflected in the dynamics of interval exchange maps. In Chapter 3 a...
- Keyword:
- Mathematics
- Subject:
- Mathematics
- Creator:
- Christopher Novak
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 09/06/2018
- Date Modified:
- 09/06/2018
- Date Created:
- 2008-05-06
- Resource Type:
- Dissertation
-
- Description:
- Let X be a quasi-projective complex variety. It follows from the work of Voevodsky that the motivic cohomology of X, denoted as $H^{p,q}(X)$ where q and p are integers with q nonnegative, can be represented in the triangulated category of motives over the field of complex numbers, denoted as $DM^{eff,-}_{Nis}$....
- Keyword:
- Mathematics
- Subject:
- Mathematics
- Creator:
- Chenghao Chu
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 08/31/2018
- Date Modified:
- 08/31/2018
- Date Created:
- 2008-05-02
- Resource Type:
- Dissertation
-
- Description:
- The Satake category is the category of perverse sheaves on the affine Grassmannian of a complex reductive group G. The global cohomology functor induces a tensor equivalence between the Satake category and the category of finite-dimensional representations of the split form of the Langlands dual group of G. We give...
- Keyword:
- Satake isomorphism, Geometric Langlands program, representation theory, and forms of reductive groups
- Subject:
- Mathematics
- Creator:
- Vivek Dhand
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 08/29/2018
- Date Modified:
- 08/29/2018
- Date Created:
- 2007-12-07
- Resource Type:
- Dissertation
-
- Description:
- Homotopy Gerstenhaber structure is shown to exist on the deformation complex of a morphism of associative algebras. The main step of the construction is extension of a B-infinity algebra by an associative algebra. Actions of B-infinity algebras on associative and B-infinity algebras are analyzed, extensions of B-infinity algebras by associative...
- Keyword:
- associative algebras and Deformations
- Subject:
- Mathematics
- Creator:
- Dennis Borisov
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 06/27/2018
- Date Modified:
- 06/27/2018
- Date Created:
- 2007-05-07
- Resource Type:
- Dissertation
-
- Description:
- We prove the L<SUP>2</SUP>-convergence of polynomial ergodic averages of multiple commuting transformations for totally ergodic systems. We show that for each set of polynomials, each average is controlled by a particular characteristic factor introduced by Host and Kra, which is an inverse limit of nilsystems. We then investigate for which...
- Keyword:
- dynamical systems and ergodic theory
- Subject:
- Mathematics
- Creator:
- Michael Charles Reed Johnson
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 06/26/2018
- Date Modified:
- 06/26/2018
- Date Created:
- 2007-05-11
- Resource Type:
- Dissertation
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