Princeton University Department of Mathematics
Overview
Works:  162 works in 169 publications in 1 language and 185 library holdings 

Genres:  Conference proceedings Periodicals 
Classifications:  QA1, 512.8 
Publication Timeline
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Most widely held works about
Princeton University
 The Princeton mathematics community in the 1930's : an oralhistory project ( Book )
 Oral history interview with John G. Kemeny by John G Kemeny John G Kemeny( )
 Princeton & mathematics; a notable record by Virginia Chaplin Virginia Chaplin( Book )
 Oral history interview with John Bardeen by John Bardeen John Bardeen( )
 Reminiscence of R. E. Greenwood by R. E Greenwood R. E Greenwood( )
 Oral history interview with Jack B. Levine by Jack B Levine Jack B Levine( )
 Reminiscence of Malcolm Robertson by Malcolm Robertson Malcolm Robertson( )
 Oral history interview with Banesh Hoffmann by Banesh Hoffmann Banesh Hoffmann( )
 Oral history interview with Albert W. Tucker by Albert W Tucker Albert W Tucker( )
 Oral history interview with Albert W. Tucker by Albert W Tucker Albert W Tucker( )
 Oral history interview with Albert W. Tucker by Albert W Tucker Albert W Tucker( )
 Oral history interview with Merrill Flood by Merrill Flood Merrill Flood( )
 Oral history interview with R. E. Greenwood by R. E Greenwood R. E Greenwood( )
 Donald C. Spencer Papers by D. C Spencer D. C Spencer( )
 Oral history interview with Albert W. Tucker by Albert W Tucker Albert W Tucker( )
 Princeton mathematics community in the 1930s ( )
 Biographical sketches of some members of the mathematics and physics faculty of Princeton University : by Katherine S Eisenhart Katherine S Eisenhart( )
 Oral history interview with S. Wylie by S Wylie S Wylie( )
 Oral history interview with James Wallace Givens, Leon Henkin, Angus Ellis Taylor, and Abraham Haskel Taub by James Wallace Givens James Wallace Givens( )
 Oral history interview with Robert J. Walker by Robert J Walker Robert J Walker( )
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Most widely held works by
Princeton University
Mathematics 108, Introduction to differential calculus
by
Princeton University(
)
2 editions published in 1937 in English and held by 12 WorldCat member libraries worldwide
2 editions published in 1937 in English and held by 12 WorldCat member libraries worldwide
Prospects in mathematics : invited talks on the occasion of the 250th anniversary of Princeton University, March 1721, 1996, Princeton University
by
Hugo Rossi(
Book
)
1 edition published in 1999 in English and held by 7 WorldCat member libraries worldwide
In celebration of Princeton University's 250th anniversary, the mathematics department held a conference entitled "Prospects in Mathematics". The purpose of the conference was to speculate on future directions of research in mathematics. This collection of articles provides a rich panorama of current mathematical activity in many research areas
1 edition published in 1999 in English and held by 7 WorldCat member libraries worldwide
In celebration of Princeton University's 250th anniversary, the mathematics department held a conference entitled "Prospects in Mathematics". The purpose of the conference was to speculate on future directions of research in mathematics. This collection of articles provides a rich panorama of current mathematical activity in many research areas
Contributions to the theory of games
(
Book
)
1 edition published in 1959 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 1959 in English and held by 6 WorldCat member libraries worldwide
Contributions to the theory of games
by
Harry Waldo Kuhn(
Book
)
1 edition published in 1957 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 1957 in English and held by 6 WorldCat member libraries worldwide
Limits and spectral sequences
by
Samuel Eilenberg(
Book
)
2 editions published in 1960 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1960 in English and held by 4 WorldCat member libraries worldwide
Some free actions of cyclic groups on spheres
by
John W Milnor(
Book
)
2 editions published in 1963 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1963 in English and held by 4 WorldCat member libraries worldwide
Effective bisector estimate with application to Apollonian circle packings
by Ilya Vinogradov(
)
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
Let Gamma < PSL(2, C) be a geometrically finite nonelementary discrete subgroup, and let its critical exponent delta be greater than 1. We use representation theory of PSL(2, C) to prove an effective bisector counting theorem for Gamma, which allows counting the number of points of Gamma in general expanding regions in PSL(2, C) and provides an explicit error term. We apply this theorem to give power savings in the Apollonian circle packing problem and related counting problems
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
Let Gamma < PSL(2, C) be a geometrically finite nonelementary discrete subgroup, and let its critical exponent delta be greater than 1. We use representation theory of PSL(2, C) to prove an effective bisector counting theorem for Gamma, which allows counting the number of points of Gamma in general expanding regions in PSL(2, C) and provides an explicit error term. We apply this theorem to give power savings in the Apollonian circle packing problem and related counting problems
An assortment of results in combinatorics and compressed sensing
by Boris Alexeev(
Book
)
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
We prove a variety of results spanning combinatorics, compressed sensing, and theoretical computer science. Our methods throughout are primarily combinatorial, but we also use algebraic techniques and occasionally estimates from analysis
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
We prove a variety of results spanning combinatorics, compressed sensing, and theoretical computer science. Our methods throughout are primarily combinatorial, but we also use algebraic techniques and occasionally estimates from analysis
Quantum Cohomology of Hypertoric Varieties and Geometric Representations of Yangians
by Michael Ben McBreen(
Book
)
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
This thesis compares two geometric constructions of a Yangian, due to Varagnolo and Nakajima on the one hand and Maulik and Okounkov on the other. It also, separately, computes the quantum cohomology of smooth hypertoric varieties, and finds a mirror formula for their quantum connection. It contains brief introductions to the background material for both problems
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
This thesis compares two geometric constructions of a Yangian, due to Varagnolo and Nakajima on the one hand and Maulik and Okounkov on the other. It also, separately, computes the quantum cohomology of smooth hypertoric varieties, and finds a mirror formula for their quantum connection. It contains brief introductions to the background material for both problems
Abelianization of stable envelopes in symplectic resolutions
by Daniel Shenfeld(
Book
)
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
Stable envelopes, introduced by Maulik and Okounkov, form a basis for the equivariant cohomology of symplectic resolutions. We study the case of Nakajima quiver varieties, where the resolution is a hyperkahler quotient. We relate the stable basis to that of the associated quotient by a maximal torus, and obtain a formula for the transition between the stable basis and the fixed point basis, using the root system and combinatorial data from the torus quotient
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
Stable envelopes, introduced by Maulik and Okounkov, form a basis for the equivariant cohomology of symplectic resolutions. We study the case of Nakajima quiver varieties, where the resolution is a hyperkahler quotient. We relate the stable basis to that of the associated quotient by a maximal torus, and obtain a formula for the transition between the stable basis and the fixed point basis, using the root system and combinatorial data from the torus quotient
Structural stability of mappings
by John Mather(
Book
)
1 edition published in 1966 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1966 in English and held by 2 WorldCat member libraries worldwide
KahlerEinstein metrics and Kstability
by
Ji Li(
)
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
In this thesis, we study several problems related to the existence problem of KahlerEinstein metric on Fano manifold. After introduction in the first chapter, in the second chapter, we review the basic theory both from PDE and variational point of view. Tian's program using finite dimensional approximation is then explained. Futaki invariant is discussed in detail for both its definition and calculation. Kstability is introduced following Tian and Donaldson. In the third chapter, we extend the basic theory to the twisted setting. As an important case, the analytic and algebraic theory are both extended to the conic setting. In the third chapter, we study the continuity method on toric Fano manifolds. We calculate the maximal value of parameter for solvability and study the limit behavior of the solution metrics. As a corollary, we prove Tian's partial C0estimate on toric Fano manifolds. The logFutaki invariant is calculated on toric Fano manifolds too. In the fourth chapter, we discuss the recent joint work with Dr. Chenyang Xu. We use Minimal Model Program (MMP) to simplify the degeneration and prove Tian's conjecture which reduce the test for Kstability to special degenerations. In the final chapter, we construct examples of rotationally symmetric solitons. These solitons are local models of special singularities of KahlerRicci flow
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
In this thesis, we study several problems related to the existence problem of KahlerEinstein metric on Fano manifold. After introduction in the first chapter, in the second chapter, we review the basic theory both from PDE and variational point of view. Tian's program using finite dimensional approximation is then explained. Futaki invariant is discussed in detail for both its definition and calculation. Kstability is introduced following Tian and Donaldson. In the third chapter, we extend the basic theory to the twisted setting. As an important case, the analytic and algebraic theory are both extended to the conic setting. In the third chapter, we study the continuity method on toric Fano manifolds. We calculate the maximal value of parameter for solvability and study the limit behavior of the solution metrics. As a corollary, we prove Tian's partial C0estimate on toric Fano manifolds. The logFutaki invariant is calculated on toric Fano manifolds too. In the fourth chapter, we discuss the recent joint work with Dr. Chenyang Xu. We use Minimal Model Program (MMP) to simplify the degeneration and prove Tian's conjecture which reduce the test for Kstability to special degenerations. In the final chapter, we construct examples of rotationally symmetric solitons. These solitons are local models of special singularities of KahlerRicci flow
FiniteSheeted Covering Spaces and Solenoids over 3manifolds
by Will Cavendish(
)
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
This thesis develops techniques for studying towers of finitesheeted covering spaces of 3manifolds. The central question we seek to address is the following: given a pi1injective continuous map ƒ : S → M of a 2manifold S into a 3manifold M, when does there exist a nontrivial connected finitesheeted covering space M' of M such that ƒ lifts to M'? We approach this problem by reformulating it in terms of isometric actions of pi1(M) on compact metric spaces. We then study regular solenoids over M, which give natural examples of compact metric spaces with isometric pi 1(M)actions. We conclude by introducing a construction that we call the mapping solenoid of a map ƒ : S → M, which can be used to derive cohomological criteria that guarantee the existence of a lift of ƒ to a nontrivial connected finitesheeted covering space of M
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
This thesis develops techniques for studying towers of finitesheeted covering spaces of 3manifolds. The central question we seek to address is the following: given a pi1injective continuous map ƒ : S → M of a 2manifold S into a 3manifold M, when does there exist a nontrivial connected finitesheeted covering space M' of M such that ƒ lifts to M'? We approach this problem by reformulating it in terms of isometric actions of pi1(M) on compact metric spaces. We then study regular solenoids over M, which give natural examples of compact metric spaces with isometric pi 1(M)actions. We conclude by introducing a construction that we call the mapping solenoid of a map ƒ : S → M, which can be used to derive cohomological criteria that guarantee the existence of a lift of ƒ to a nontrivial connected finitesheeted covering space of M
Statistical research at Princeton University, supported by the Office of Naval Research, 19461956
by
Princeton University(
Book
)
1 edition published in 1956 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1956 in English and held by 2 WorldCat member libraries worldwide
Three perspectives on n points in P(n2)
by Kevin H Wilson(
Book
)
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
Finally, in the last chapter, we briefly discuss the representation theoretic import of the sextic resolvent of a quintic field. At this time, we have not been able to use this to extend Bhargava's parameterization of quintic rings to arbitrary base schemes in the spirit of Deligne and Wood, but we believe that this chapter forms an important start in that direction
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
Finally, in the last chapter, we briefly discuss the representation theoretic import of the sextic resolvent of a quintic field. At this time, we have not been able to use this to extend Bhargava's parameterization of quintic rings to arbitrary base schemes in the spirit of Deligne and Wood, but we believe that this chapter forms an important start in that direction
Variations on a theorem of Tate
by Stefan Patrikis(
)
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
Let F be a number field, with absolute Galois group G. For any homomorphism r of G valued in the ladic points of a linear algebraic group H, we consider lifting problems through covers H' of H with central torus kernel. By a theorem of Tate, elaborated by B. Conrad, any such continuous homomorphism to H lifts to H'. Largely motivated by a question of Conrad, who asked when geometric homomorphisms (in the sense of FontaineMazur) should admit geometric liftings, we address a number of Galoistheoretic, automorphic, and motivic variants of the lifting problem
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
Let F be a number field, with absolute Galois group G. For any homomorphism r of G valued in the ladic points of a linear algebraic group H, we consider lifting problems through covers H' of H with central torus kernel. By a theorem of Tate, elaborated by B. Conrad, any such continuous homomorphism to H lifts to H'. Largely motivated by a question of Conrad, who asked when geometric homomorphisms (in the sense of FontaineMazur) should admit geometric liftings, we address a number of Galoistheoretic, automorphic, and motivic variants of the lifting problem
Some Generalizations of the Hopf Extension Theorem
by Daniel D Kahn(
Book
)
1 edition published in 1957 in English and held by 1 WorldCat member library worldwide
1 edition published in 1957 in English and held by 1 WorldCat member library worldwide
Etale covering between resolution of isolated singularities and GaffneyLazarsfeld theorem for homogeneous spaces
by YuChao Tu(
)
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
In the third chapter, we begin with the notions of local degrees and higher ramification loci in order to obtain the GaffneyLazarsfeld theorem on projective spaces and Grassmannians. After some fundamental properties of homogeneous spaces, we give a generalization of the GaffneyLazarsfeld theorem for homogeneous spaces of Picard number one
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
In the third chapter, we begin with the notions of local degrees and higher ramification loci in order to obtain the GaffneyLazarsfeld theorem on projective spaces and Grassmannians. After some fundamental properties of homogeneous spaces, we give a generalization of the GaffneyLazarsfeld theorem for homogeneous spaces of Picard number one
The Efficiency of Merrill's Algorithm and the Newton Methods for the Computation of Fixed Points
by Kenneth Boese(
Book
)
1 edition published in 1982 in English and held by 1 WorldCat member library worldwide
1 edition published in 1982 in English and held by 1 WorldCat member library worldwide
Senior theses presented to the Department of Mathematics
by
Princeton University(
)
in English and held by 1 WorldCat member library worldwide
in English and held by 1 WorldCat member library worldwide
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Department of Mathematics of the Princeton University.
Dept. of Mathematics, Princeton University.
Princeton University Dept. of Mathematics
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