Princeton University Department of Mathematics
Overview
Works:  189 works in 202 publications in 1 language and 281 library holdings 

Genres:  Conference papers and proceedings 
Classifications:  QA1, 510 
Publication Timeline
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Most widely held works about
Princeton University
 Oral history interview with John Bardeen by John Bardeen( )
 The Princeton mathematics community in the 1930's : an oralhistory project( Book )
 Oral history interview with John G. Kemeny by John G Kemeny( )
 Princeton & mathematics; a notable record by Virginia Chaplin( Book )
 Oral history interview with Albert W. Tucker by Albert W Tucker( )
 Oral history interview with Joseph Francis Daly and Churchill Eisenhart by Joseph Francis Daly( )
 Oral history interview with Robert J. Walker by Robert J Walker( )
 Oral history interview with Stephen Cole Kleene and J. Barkley Rosser by Stephen Cole Kleene( )
 Reminiscence of Malcolm Robertson by Malcolm Robertson( )
 Oral history interview with Deane Montgomery by Deane Montgomery( )
 Princeton mathematics community in the 1930s( )
 Oral history interview with R.E. Greenwood by R. E Greenwood( )
 Oral history interview with Albert W. Tucker by Albert W Tucker( )
 Oral history interview with Merrill Flood by Merrill Flood( )
 Oral history interview with Albert W. Tucker by Albert W Tucker( )
 Oral history interview with William Larkin Duren, Nathan Jacobson, and E.J. McShane by William Larkin Duren( )
 Oral history interview with Albert W. Tucker by Albert W Tucker( )
 Biographical sketches of some members of the mathematics and physics faculty of Princeton University : by Katherine S Eisenhart( )
 Oral history interview with James Wallace Givens, Leon Henkin, Angus Ellis Taylor, and Abraham Haskel Taub by Wallace Givens( )
 Donald C. Spencer Papers by D. C Spencer( )
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Most widely held works by
Princeton University
Convex cones, sets, and functions by
W Fenchel(
Book
)
1 edition published in 1953 in English and held by 44 WorldCat member libraries worldwide
1 edition published in 1953 in English and held by 44 WorldCat member libraries worldwide
On the development and applications of linear programming in the USSR by
G. Sh Rubinshteĭn(
Book
)
2 editions published in 1960 in English and held by 8 WorldCat member libraries worldwide
2 editions published in 1960 in English and held by 8 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 by
Robert J Aumann(
Book
)
1 edition published in 1959 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 1959 in English and held by 5 WorldCat member libraries worldwide
Contributions to the theory of games by
Claude Berge(
Book
)
1 edition published in 1957 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1957 in English and held by 4 WorldCat member libraries worldwide
Mathematics 108, Introduction to differential calculus by
Princeton University(
Book
)
2 editions published in 1937 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1937 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 3 WorldCat member libraries worldwide
2 editions published in 1963 in English and held by 3 WorldCat member libraries worldwide
Limits and spectral sequences by
Samuel Eilenberg(
Book
)
2 editions published in 1960 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1960 in English and held by 3 WorldCat member libraries worldwide
A bound on the average rank of jinvariant zero elliptic curves by Samuel Ruth(
Book
)
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
In this thesis, we prove that the average rank of jinvariant 0 elliptic curves, when ordered by discriminant, is bounded above by 3. This work follows from work of Bhargava and Shankar relating elements of the 2Selmer groups of elliptic curves with equivalence classes of certain binary quartic forms. We also count the number of equivalence classes of these binary quartic forms. This step involves counting the number of points on a quadric in a homogenously expanding noncompact region. To count the number of points on this quadric, we use a modified version of the circle method. This work also has an application to the statistics of the class group of certain pure cubic fields
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
In this thesis, we prove that the average rank of jinvariant 0 elliptic curves, when ordered by discriminant, is bounded above by 3. This work follows from work of Bhargava and Shankar relating elements of the 2Selmer groups of elliptic curves with equivalence classes of certain binary quartic forms. We also count the number of equivalence classes of these binary quartic forms. This step involves counting the number of points on a quadric in a homogenously expanding noncompact region. To count the number of points on this quadric, we use a modified version of the circle method. This work also has an application to the statistics of the class group of certain pure cubic fields
On moduli spaces of real curves in symplectic manifolds by Mohammad Farajzadeh Tehrani(
Book
)
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
Given a symplectic manifold (X, o), an almost complex structure J, and an antisymplectic involution & phis;, we study genus zero real Jholomorphic curves in X. There are two types of such curves, those that can be divided into two Jholomorphic discs and those that cannot. Moduli spaces of Jholomorphic discs are more studied in the literature; in this case, we develop and use some degeneration techniques to add to the previous results and get a better understanding of these moduli spaces. We also study the second case, for which the orientation problem is different and define (and calculate) some invariants using these moduli spaces. As shown in this thesis, these two cases are tied together and often need to be combined to get a fully welldefined theory
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
Given a symplectic manifold (X, o), an almost complex structure J, and an antisymplectic involution & phis;, we study genus zero real Jholomorphic curves in X. There are two types of such curves, those that can be divided into two Jholomorphic discs and those that cannot. Moduli spaces of Jholomorphic discs are more studied in the literature; in this case, we develop and use some degeneration techniques to add to the previous results and get a better understanding of these moduli spaces. We also study the second case, for which the orientation problem is different and define (and calculate) some invariants using these moduli spaces. As shown in this thesis, these two cases are tied together and often need to be combined to get a fully welldefined theory
Structural approaches to spin glasses and optimization problems by
Luca De Sanctis(
)
1 edition published in 2005 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 2 WorldCat member libraries worldwide
Variations on a theorem of Tate by Stefan Patrikis(
Book
)
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
A crystalline approximation theorem for hypersurfaces by John Matthew Sullivan(
)
1 edition published in 1990 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1990 in English and held by 2 WorldCat member libraries worldwide
Decay of correlations for the RauzyVeechZorich induction map and the central limit theorem for the Teichmul̈ler geodesic
flow by
Alexander I Bufetov(
)
1 edition published in 2005 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 2 WorldCat member libraries worldwide
The average rank of elliptic curves over number fields by Arul Shankar(
)
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
In joint work with Manjul Bhargava, we proved that the average rank of rational elliptic curves, when ordered by their heights, is bounded above by 1.5. This result was accomplished by using Bhargava's geometryofnumbers methods to obtain asymptotics for the number of GL2( Z )orbits on integral binary quartic forms having bounded invariants
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
In joint work with Manjul Bhargava, we proved that the average rank of rational elliptic curves, when ordered by their heights, is bounded above by 1.5. This result was accomplished by using Bhargava's geometryofnumbers methods to obtain asymptotics for the number of GL2( Z )orbits on integral binary quartic forms having bounded invariants
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
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
Some Results on a Fully Nonlinear Equation in Conformal Geometry by Nicholas William Reichert(
Book
)
1 edition published in 2014 in English and held by 2 WorldCat member libraries worldwide
Second, we study the question of solving sigma k = constant on nmanifolds M, the "sigma kYamabe problem", when k = 2 and n = 3. The sigmakYamabe problem has been studied for many values of n and k before (by Li and Li, by Guan and Wang, by Gursky and Viaclovsky, by Sheng, Trudinger, and Wang, and by Trudinger and Wang, among others); however, some cases remain open. The case where n <2k is unresolved in general. A perhaps more natural question to consider in this case is solving v2k = constant, for n <2k, where v2k are the renormalized volume coefficients studied by Graham and by Chang and Fang. Unfortunately, the approach used for other values of n and k does not apply in this final casefor v 2k, one cannot use the local estimates of Guan and Wang and of Chen. This is because the local estimates use algebraic properties of sigmak which do not hold for v 2k. Though the sigma2Yamabe problem in dimension 3 has been studied before, we study an alternative approach which avoids the use of the local estimates. We hope this approach may prove useful for resolving the question of solving v2 k = constant
1 edition published in 2014 in English and held by 2 WorldCat member libraries worldwide
Second, we study the question of solving sigma k = constant on nmanifolds M, the "sigma kYamabe problem", when k = 2 and n = 3. The sigmakYamabe problem has been studied for many values of n and k before (by Li and Li, by Guan and Wang, by Gursky and Viaclovsky, by Sheng, Trudinger, and Wang, and by Trudinger and Wang, among others); however, some cases remain open. The case where n <2k is unresolved in general. A perhaps more natural question to consider in this case is solving v2k = constant, for n <2k, where v2k are the renormalized volume coefficients studied by Graham and by Chang and Fang. Unfortunately, the approach used for other values of n and k does not apply in this final casefor v 2k, one cannot use the local estimates of Guan and Wang and of Chen. This is because the local estimates use algebraic properties of sigmak which do not hold for v 2k. Though the sigma2Yamabe problem in dimension 3 has been studied before, we study an alternative approach which avoids the use of the local estimates. We hope this approach may prove useful for resolving the question of solving v2 k = constant
Spin field equations and YangMills equation by
WeiTong Shu(
)
1 edition published in 1990 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1990 in English and held by 2 WorldCat member libraries worldwide
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
We compute the transition matrix explicitly in the case of cotangent bundles to partial flag varieties, and show that for Grassmannians, it is given by rational Schur polynomials. This recovers in a geometric way the diagonalization of the Hamiltonian in the XXX spin chain. As a second application, we study the case of the Hilbert scheme of points on the plane, and obtain a novel formula expressing Schur polynomials in terms of Jack polynomials
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
We compute the transition matrix explicitly in the case of cotangent bundles to partial flag varieties, and show that for Grassmannians, it is given by rational Schur polynomials. This recovers in a geometric way the diagonalization of the Hamiltonian in the XXX spin chain. As a second application, we study the case of the Hilbert scheme of points on the plane, and obtain a novel formula expressing Schur polynomials in terms of Jack polynomials
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fewer
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Related Identities
 Fenchel, W. (Werner) 1905 Author
 Blackett, Donald W.
 Tucker, Albert W. (Albert William) 19051995 Author
 Aspray, William
 United States Office of Naval Research
 Milnor, John W. (John Willard) 1931 Author
 George Washington University Logistics Research Project
 Institute for Advanced Study (Princeton, N.J.)
 Rubinshteĭn, Gennadiĭ Shlemovich Author
 Princeton University
Associated Subjects
Algebraic topology Buildings Chance China Church, Alonzo, Complexes Convex domains Convex functions Convex sets Convex surfaces Differential calculus Differential topology Distance geometry Economics Einstein, Albert, Eisenhart, Luther Pfahler, Electrical engineeringStudy and teaching Games of chance (Mathematics) Game theory Geometry, Differential Geometry, Modern Geophysics Graduate students Institute for Advanced Study (Princeton, N.J.) Institute for Advanced Study (Princeton, N.J.).School of Mathematics Kemeny, John G Logic, Modern Logicians Logistics Mathematicians Mathematics MathematicsStudy and teaching New JerseyPrinceton Princeton University Princeton University.Department of Mathematics Princeton University.Department of Physics Robertson, H. P.(Howard Percy), Slater, John C.(John Clarke), Solid state physics Stanford University.Department of Mathematics StatisticsResearch Topology Turing, Alan Mathison, Ulam, Stanislaw M United States Universities and collegesFaculty Van Vleck, J. H.(John Hasbrouck), Veblen, Oswald, Von Neumann, John, Wigner, Eugene Paul,
Alternative Names
Department of Mathematics
Department of Mathematics of the Princeton University.
Dept. of Mathematics, Princeton University.
Mathematics Department
Princeton University Dept. of Mathematics
Princeton University Mathematics Department
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