Recent PhDs

The following is a list of the Ph. D. degrees awarded by academic year from Fall 2007 - Summer 2015 (in descending order) including the title of the dissertation, the thesis advisor(s) and when possible, the first place of employment.


Pedro Acosta
A general Landau-Ginzburg/Gromov-Witten correspondence
(Y. Ruan, 2015) University of Minnesota

David Benson-Putnins
Volumes and integer points of multi-index transportation polytopes
(A. Barvinok, 2015) Jane Street Capital

Andrew Brouwer (AIM)
Models of HPV as an infectious disease and as an etiological agent of cancer
(M. Eisenberg & R. Meza) University of Michigan School of Public Health

Daniel DeWoskin (AIM)
Multiscale modeling of coupled oscillators with applications to the mammalian circadian clock
(D. Forger & S. Schnell) University of California, Davis

Brittan Farmer (AIM)
Modeling and simulation of carbon nanotube growth
(S. Esedoglu & J. Hart) University of Minnesota

Balin Fleming
Arc schemes in logarithmic algebraic geometry
(K. Smith) University of British Columbia

Purvi Gupta
Fefferman's hypersurface measure and volume approximation problems
(D. Barrett) University of Western Ontario

Daniel Hathaway
Domination of functions
(A. Blass, 2015) University of Denver

Zhibek Kadyrsizova
Tight closure, F-purity, and varieties of nearly commuting matrices
(M. Hochster)

Giwan Kim
Richardson varieties in a toric degeneration of the flag variety
(D. Speyer)

Juan Felipe Perez
On connections between invariants of singularities in zero and positive characteristics
(M. Mustata)

Russell Ricks
Flat strips, Bowen-Margulis measures, and mixing of the geodesic flow for rank one CAT(0) spaces
(R. Spatzier) Binghamton University

Brandon Seward
Krieger's finite generator theorem for ergodic actions of countable groups
(R. Spatzier) Hebrew University of Jerusalem

Ariel Shnidman
Heights of generalized Heegner cycles
(K. Prasanna) Boston College

Yi Su
Electrical networks and electrical lie theory of classical types
(T. Lam)

 Brooke Ullery
Tautological vector bundles on the Hilbert scheme of points and the normality of secant varieties
(K. Smith) University of Utah

Alfredo Wetzel (AIM)
Three stratified fluid models: Benjamin-Ono, Tidal Resonance, and Quasi-Geostrophy
(P. Miller & B. Arbic)

Tengren Zhang
Degeneration of Hitchin representations
(D. Canary) California Institute of Technology

Yuchong Zhang (AIM)
Problems in mathematical finance related to transaction costs and model uncertainty
(E. Bayraktar & U. Rajan) Columbia University

Xiaolei Zhao
Topological Abel-Jacobi mapping and Jacobi inversion
(K. Smith and R. Lazarsfeld) Northeastern University

Zhou Zhou (AIM)
Topics in optimal stopping and fundamental theorem of asset pricing
(E. Bayraktar & H. Ahn) University of Minnesota

2013 - 2014

Harry Altman
Integer Complexity, Addition Chains, and Well Ordering
(J. Lagarias)

Jeffrey Calder (AIM)
Hamilton-Jacobi Equations for Sorting and Percolation Problems
(S. Esedoglu & A. Hero) University of California, Berkeley

Kevin Carde
Cluster Algebras and Classical Invariant Rings
(S. Fomin) Canada/USA Mathcamp

Michael Chmutov
The Structure of W-Graphs Arising in Kazhdan-Lusztig Theory
(J. Stembridge) University of Minnesota

Emily Clader
The Landau-Ginzburg/Calabi-Yau Correspondence for Certain Complete Intersections
(Y. Ruan) ETH Zurich - Institute for Theoretical Studies

Nicolas Ford
Geometric Shifts and Positroid Varieties
(D. Speyer) Jane Street Capital

Bich (Becky) Hoai
On Symplectic Invariants Associated to Zoll Manifolds
(D. Burns) Fedearal Researve Bank of St. Louis

June Huh
Rota's Conjecture and Positivity of Algebraic Cycles in Toric Varieties
(M. Mustata) Clay Mathematics Institute

Rafe Kinsey
A Priori Estimates for Two-Dimensional Water Waves with Angled Crests
(S. Wu)

Kin Kwan Leung
Complex Geometric Invariants Associated to Zoll Manifolds
(D. Burns) University of Toronto

Sijun Liu
Functional Equations Involving Laurent Polynomials and Meromorphic Functions, with Applications to Dynamics and Diophantine Equations
(M. Zieve) Oracle

Zhipeng Liu
Discrete Toeplitz Determinants and their Applications
(J. Baik) New York University

Linquan Ma
The Frobenius Endomorphism and Multiplicities
(M. Hochster) Purdue University

Hieu Ngo
Generalizations of the Lerch Zeta Function
(J. Lagarias) Texas A&M University Qatar

Nathan Priddis
A Landau-Ginzburg/Calabi-Yau Correspondence for the Mirror Quintic
(Y. Ruan) Leibniz University of Hannover

Maria Riolo (AIM)
Topics in Structured Host-Antagonist Interactions
(C. Doering & P. Rohani)

Geoffrey Scott
Torus Actions and Singularities in Symplectic Geometry
(D. Burns) African Institute for Mathematical Sciences

Ashley Wheeler
Ideals Generated by Principal Minors
(M. Hochster) University of Arkansas

Mary Wootters
Any Errors in this Dissertation are Probably Fixable: Topics in Probability and Error Correcting Codes
(M. Strauss) Carnegie Mellon University

Jingchen Wu (AIM)
Some Problems in Stochastic Control Theory Related to Inventory Management and Coarsening
(J. Conlon & X. Chao)

Yilun Wu (AIM)
On Existence and Properties of Rotating Star Solutions to the Euler-Poisson Equations
(J. Smoller & F. Adams)

Xin Zhou
Asymptotics of Equivariant Syzygies
(R. Lazarsfeld & M. Mustata) Global Atlantic

Andrew Zimmer
Rigidity in Complex Projective Space
(R. Spatzier) University of Chicago


2012 - 2013

William Abram
Equivariant Complex Cobordism
(I. Kriz) Hillsdale College

Samuel Altschul
Endoscopy for Nilpotent Orbits of G_2
(S. DeBacker) Harvard University

Jennifer Beichman
Nonstandard Dispersive Estimates and Linearized Water Waves
(S. Wu) University of Wisconsin Madison

Peter Bosler (AIM)
Particle Methods for Geophysical Flow on the Sphere
(R. Krasny & C. Jablonowski) University of Michigan

Ernest Hunter Brooks
Generalized Heegner Cycles, Shimura Curves, and Special Values of p-ADIC L-Functions
(K. Prasanna) Federale de Lausanne

Sohhyun Chung (AIM)
The Impact of Volcker Rule on Bank Profits and Default Probabilities
(J. Conlon & J. Keppo)

William Gignac
Equidistribution of Preimages in Nonarchimedean Dynamics
(M. Jonsson) Ecole Polytechnique/Georgia Tech

Huaiying Gu (AIM)
Value-At-Risk (VaR) and Dynamic Portfolio Selection
(J. Conlon & H. Li) Key Corp

Shawn Henry
Classifying Topoi and Preservation of Higher Order Logic by Geometric Morphisms
(A. Blass) Colorado University

Yu-Jui Huang (AIM)
Topics in Stochastic Control with Applications to Finance
(E. Bayraktar & H. Li) Dublin City University

Jae Kyoung Kim (AIM)
Mathematical Modeling and Analysis of Cellular Clocks
(D. Forger & V. Booth) Ohio State University

Ross Kravitz
Problems in Optimal Stopping and Control
(E. Bayraktar) Kabam

Sara Lapan
On the Existence of Attracting Domains for Maps Tangent to the Identity
(M. Jonsson) Northwestern University

Seung Jin Lee
Centrally Symmetric Polytopes with Many Faces
(A. Barvinok) Korea Institute for Advanced Study

Sarah Mayes
The Asymptotic Behavior of Generic Initial Systems
(K. Smith) Quest University Canada

Jeffrey Meyer
On the Totally Geodesic Commensurability Spectrum of an Arithmetic Locally Symmetric Spaces
(R. Spatzier & M. Stover) University of Oklahoma

Alexander Mueller
Applications of Generalized Fermat Varieties to Zeta Functions of Artin-Schreier Curves
(M. Zieve) Less Annoying Software

Luis Nunez Betancourt
Finiteness Properties of Local Cohomology
(M. Hochster) University of Virginia

Kristofer-Roy Reyes (AIM)
Fast Kinetic Monte Carlo Simulations: Theory, Implementation and Applications
(P. Smereka & J. Mirecki-Millunchick)

Joseph Roberts
Steady and Self-similar Solutions to Two-dimensional Hyperbolic Conservation Laws
(V. Elling) Pennsylvania State University

Julian Rosen
The Arithmetic of Multiple Harmonic Sums
(J. Lagarias) University of Waterloo

Burhan Sadiq (AIM)
Finite Difference Methods, Hermite Interpolation and Quasi-Uniform Spectral Schemes (QUSS)
(D. Viswanath & J. Boyd)

Zachary Scherr
Rational Polynomial Pell Equations
(M. Zieve) University of Pennsylvania

Paul Shearer (AIM)
Separable Inverse Problems, Blind Deconvolution, and Stray Light Correction for Extreme Ultraviolet Solar Images
(A. Gilbert, R. Frazin & A. Hero) University of Michigan

Yefeng Shen
Gromov-Witten Theory of Elliptic Orbifold Projective lines
(Y. Ruan) Kavli IPMU

Mark Shoemaker
A Mirror Theorem for the Mirror Quintic
(Y. Ruan) University of Utah

Jordan Watkins
The Rank Rigidity Theorem for Manifolds with No Focal Points
(R. Spatzier)

Zhixian Zhu
Topics in Singularities and Jet Schemes
(M. Mustata) KIAS

2011 - 2012

Taeyong Ahn
Foliation Structure for Generalized Henon Mappings
(J. Fornaess) POSTECH

Aubrey da Cunha
Turing Machines, Cayley Graphs, and Inescapable Groups
(A. Blass) MathWorks

Elizabeth DeWitt
Identities Relating Schur s-Functions and Q-Functions
(J. Stembridge) University of Maryland University College

Steven Flores (AIM)
Correlation Functions in Two-Dimensional Critical Systems with Conformal Symmetry
(C. Doering & R. Ziff)

Aurel (Mihai) Fulger
Local volumes
(R. Lazarsfeld) Princeton University

Max Glick
The Pentagram Map: Combinatorial and Geometric Perspectives
(S. Fomin) Mathematical Sciences Research Institute

Ashley Holland (AIM)
Penalized Spline Estimation in the Partially Linear Model
(V. Young & M. Cataneo) Grace College

Xueying Hu (AIM)
Essays in Financial and Insurance Mathematics
(E. Bayraktar & H. Li) Goldman Sachs

Geri Izbicki Jennings (AIM)
Efficient Numerical Methods for Water Wave Propagation in Unbounded Domains
(S. Karni & R. Beck) University of Massachusetts

Robin Lassonde
Splittings of Non-Finitely Generated Groups
(G. P. Scott) East Agile

Michelle Lee
Dynamics on the PSL(2, C)-character variety of certain hyperbolic 3-manifolds
(R. Canary) University of Maryland

Matthew Masarik (AIM)
Decay of Solutions to the Wave Equation in Static Spherically Symmetric Spacetimes
(J. Smoller & M. Volonteri) SRI International

Lindsey McCarty (AIM)
Preemptive Rerouting of Airline Passengers under Uncertain Delays
(D. Viswanath & A. Cohn) Cedarville University

Andrey Mishchenko
Rigidity of Thin Disk Configurations
(J. Lagarias) UCLA IPAM

Ajinkya More
Symbolic Powers and other Contractions of Ideals in Noetherian Rings
(M. Hochster) ZL Technologies Inc

Darragh Rooney (AIM)
Control of Finite-Dimensional Quantum Systems under Lindblad Dissipation
(A. Bloch & C. Rangan) Universitat Wurzburg

Jordan Sahattchieve
Solutions to Two Open Problems in Geometric Group Theory
(G. P. Scott) William Rainey Harper College

Dave Starinshak (AIM)
Level Set Methods for Radiative Shock Hydrodynamics
(S. Karni & K. Powell) Lawrence Livermore National Laboratory

Michael Von Korff
The F-Signature and Frobenius Splitting on Toric Varieties
(K. Smith) Reasoning Mind

Nina White
Bounds on Eigenvalues of the Laplace-Beltrami Operator for Certain Classes of Hyperbolic 3-manifolds
(J. Souto & R. Canary) University of Michigan

Jared Whitehead (AIM)
Topics in Geophysical Fluid Dynamics
(C. Doering & R. Rood) Los Alamos National Laboratory

2010 - 2011

Florian Block
Plane Curves, Node Polynomials, and Floor Diagrams
(S. Fomin) University of Warwick

Eugene Eisenstein
Inversion of Adjunction in High Codimension
(R. Lazarsfeld) Goldman Sachs

Matthew Elsey (AIM)
Algorithms for Multiphase Motion with Applications to Materials Science
(S. Esedoglu & W. Lu) Courant Institute, NYU

Timothy Ferguson
Extremal Problems in Bergman Spaces
(P. Duren) Vanderbilt University

Jose Gonzalez
Toric Projective Bundles
(M. Mustata) University of British Columbia

Daniel Hernandez
$F$-Purity for Hypersurfaces
(K. Smith) University of Minnesota

Gerardo Hernandez-Duenas
An Algebra of Singular Semi-classical Pseudodifferential Operators, and Numerical Methods for Shallow Water and Porous Media Flows
(A. Uribe & S. Karni) University of Wisconsin

Brian Jennings (AIM)
Generalized Lagrangian States and Their Propagation in Bargmann Space
(A. Uribe & E. Geva) Westfield State University

Harlan Kadish
Complexity in Invariant Theory
(H. Derksen) Texas A&M University

Hyosang Kang
Cofinite Classifying Spaces for Lattices in R-Rank One Semisimple Lie Groups
(L. Ji) Korea Institute for Advanced Study

Daniel Kneezel
Verlinde K-Theory
(I. Kriz) Art of Problem Solving

Manuel Rodrigo Parra
Currents and Equidistribution in Holomorphic Dynamics
(M. Jonsson) MathWorks

Ricardo Portilla
Finite Order Automorphisms and a Parametrization of Nilpotent Orbits in P-Adic Lie Algebras
(S. DeBacker)  Celerity

Austin Shapiro
Independence Models for Integer Points of Polytopes
(A. Barvinok) Art of Problem Solving

Xinyun Sun
CM Lifting of Albelian Varieties
(B. Conrad) 

Nathan Totz
A Rigorous Justification of the Modulation Approximation to the 2D Full Water Wave Problem
(S. Wu) Duke University

Chelsea Walton
On Degenerations and Deformations of Sklyanin Algebras
(K. Smith & J. Stafford)  University of Washington

Ting Wang (AIM)
Stochastic Analysis of Insurance Products
(V. Young & H. Li) Goldman Sachs

Benjamin Weiss
Diophantine Equations with Two Separated Variables
(J. Lagarias & M. Zieve) Technion

Emily Witt
Local Cohomology and Group Actions
(M. Hochster) University of Minnesota

Qian Yin
Lattes Maps and Combinatorial Expansion
(M. Bonk & M. Zieve) MSRI & University of Chicago

Hsu-Wen Young
Components of Algebraic Sets of Commuting and Nearly-Commuting N-Tuples of Matrices
(M. Hochster) National Taiwan University

Crystal Zeager
The Azukawa Metric and the Pluricomplex Green Function
(J. Fornaess) McKinsey & Co

2009 - 2010

Henry Boateng (AIM)
Cartesian Treecode Algorithms for Electrostatic Interactions in Molecular
Dynamics Simulations
(R. Krasny & E. Geva) University of Michigan

Elizabeth Chen
A Picturebook of Tetrahedral Packings
(J. Lagarias) Harvard University

Jiarui Fei
General Presentations of Algebras
(H. Derksen) University of California- Riverside

Johnson Jia
The Arithmetic of the Yoshida Lift
(C. Skinner) PIMS/University of British Columbia

Brian Jurgelewicz
McKay's Correspondence for Klein's Quartic Curve
(I. Dolgachev)

Marc Krawitz
FJRW Rings and Landau-Ginzburg Mirror Symmetry
(Y. Ruan) McKinsey & Company

Catherine Kublik (AIM)
Topics in PDE-Based Image Processing
(S. Esedoglu & J. Fessler) University of Texas at Austin

Victor Lozovanu
Invariants in Algebraic Geometry
(R. Lazarsfeld) Queen’s University

Johanna Mangahas
A Recipe for Short-word Pseudo-Anosovs, and More
(J. Souto) Brown University

Tomoki Ohsawa (AIM)
Nonholonomic and Discrete Hamilton-Jacobi Theory
(A. Bloch & L. Pando-Zayas) University of California at San Diego

Kyle Ormsby
Computations in Stable Motivic Homotopy Theory
(I. Kriz) Massachusetts Institute of Technology

Felipe Ramirez
Smooth Cocycles over Homogeneous Dynamical Systems
(R. Spatzier) University of Bristol, UK

Nicholas Rupprecht
Effective Correspondents to Cardinal Characteristics in Cichon's Diagram
(A. Blass) Virtu Financial LLC

Luis Serrano
Non-Commutative Schur P-Functions and the Shifted Plactic Monoid
(S. Fomin) University of Quebec at Montreal

Sourya Shrestha (AIM)
Modeling Transmission and Evolutionary Dynamics of the Infectious Diseases
(P. Nelson & A. King) University of Michigan

Kelli Talaska
Positivity in Real Grassmannians: Combinatorial Formulas
(S. Fomin) University of California at Berkeley

Kevin Tucker
Jumping Numbers and Multiplier Ideals on Algebraic Surfaces
(K. Smith) University of Utah

Lei Wang (AIM)
Radial Basis Functions and Vortex Methods and their Application to Vortex Dynamics on a Rotating Sphere
(R. Krasny & J. Boyd) Argonne National Laboratory

Marshall Williams
Metric Currents and Differentiable Structures
(M. Bonk & J. Heinonen) University of Illinois at Chicago

Brian Wyman
Polynomial Decomposition over Rings
(M. Zieve) PNYLAB, LLC

Zhengjie Xu (AIM)
Asymptotic Analysis and Numerical Analysis of the Benjamin-Ono Equation
(P. Miller & J. Boyd) Bloomberg

2008 - 2009

Tigran Ananyan
Topics in Tight Closure Theory
(M. Hochster) Adrian College

David Anderson
Degeneracy and G_2 Flags
(W. Fulton) University of Washington

Arvind Baskaran (AIM)
Modeling and Simulation of Hetero-epitaxial Growth
(P. Smereka & K. Garikipati) Institute for Pure and Applied Mathematics at UCLA

Jonathan Bober
Integer Ratios of Factorials, Hypergeometric Series, and Related Step Functions
(J. Lagarias) Institute for Advanced Study

Katarina Bodova (AIM)
Topics in Applied Stochastic Dynamics
(C. Doering & A. Amirdjanova) Comenius University

David Constantine
Hyperbolic Rank-Rigidity and Compact Forms of Homogeneous Spaces
(R. Spatzier) University of Chicago

Ellen Eischen
P-adic Differential Operators on Automorphic Forms and Applications
(N. Ramsey & C. Skinner) Northwestern University

Oscar Fernandez (AIM)
The Hamiltonization of Nonholonomic Systems and its Applications
(A. Bloch & A. Rojo) University of Michigan

Leo Goldmakher
Multiplicative Mimicry and Improvements of the Polya-Vinogradov Theorem
(J. Lagarias & K. Soundararajan) University of Toronto

Russell Golman (AIM)
Essays on Population Learning Dynamics and Boundedly Rational Behavior
(A. Blass & S. Page) Carnegie Mellon University

Hester Graves
On Euclidean Ideal Classes
(N. Ramsey) Queen’s University

Christopher Hammond
Invariants of Transformation Groups Acting on Real Hypersurfaces in Complex Spaces
(D. Barrett) Texas A&M University

Kyle Hofmann
Triangulation of Locally Semi-Algebraic Spaces
(M. Mustata) National Security Agency

Paul Johnson
Equivariant Gromov-Witten Theory of One Dimensional Toric Stacks
(Y. Ruan) Imperial College

Shin-Yao Jow
Mori Dream Spaces and Okounkov Bodies
(R. Lazarsfeld) University of Pennsylvania

Wansu Kim
Galois Deformation Theory for Norm Fields and its Arithmetic Applications
(B. Conrad & S. DeBacker) Imperial College

Ryan Kinser
Rank Functors and Representation Rings of Quivers
(H. Derksen) University of Connecticut

Cagatay Kutluhan
Floer Homology and Symplectic Forms on S^1 X M^3
(D. Burns) MSRI

Michael Lieberman
Topological and Category-Theoretic Aspects of Abstract Elementary Classes
(A. Blass) University of Pennsylvania

Aaron Magid
Deformation Spaces of Kleinian Surface Groups are not Locally Connected
(R. Canary) University of Maryland

Ray Maleh (AIM)
Fast Sparse Approximation Algorithms for Medical Imaging
(A. Gilbert & J. Fessler) L3 Communications

Jessica Metcalf-Burton
Information Rates for Secret Sharing Over Various Access Structures
(A. Blass)

Marie Snipes
Flat Forms in Banach Spaces
(M. Bonk & J. Heinonen) Kenyon College

Alan Stapledon
The Geometry and Combinatorics of Ehrhart $\delta$-Vectors
(M. Mustata) MSRI

Richard Vasques (AIM)
Anisotropic Diffusion of Neutral Particles in Stochastic Media
(C. Doering & E. Larsen) McKinsey & Company

Liz Vivas
Fatou Bieberbach Domains and Automorphisms Tangent to the Identity
(B. Stensones) Purdue University

Michael Weiss
Mathematical Sense, Mathematical Sensibility: The Role of the secondary Geometry Course in Teaching Students to be like Mathematicians
(H. Bass) Oakland University

Hao Xing
Analysis of the Option Prices in Jump Diffusion Models
(E. Bayraktar) London School of Economics

2007 - 2008

Amy Bauer (AIM)
A Multi-Scale Cell-Based Model to simulated and Elucidate the Mechanisms Controlling Tumor-Induced Angiogenesis
(T. Jackson & Y. Jiang) Los Alamos National Laboratory

Oscar Felgueiras
The Ample Cone for a Morphism
(R. Lazarsfeld) Universidade do Porto

Sara Gentry (AIM)
Mathematical Modeling of Mutation Acquisition in Hierarchical Tissues: Quantification of the Cancer Stem Cell Hypothesis
(T. Jackson & S. Morrison) University of Michigan

Jose Gomez-Guerra
Models of Twisted K-Theory
(I. Kriz) University of British Columbia

Jasun Gong
Derivations on Metric Measure Spaces
(M. Bonk & J. Heinonen) University of Pittsburgh

Mark Iwen (AIM)
Algorithmic Compressed Sensing with Applications
(M. Strauss & J. Patel) Institute for Mathematics and its Applications

Harsh Jain
Quantitative Modeling of Molecular Pathways Associated with Intratumoral Angiogensis
 (T. Jackson) Frankfurt Institute of Advanced Studies, Johann Wolfgang Goethe University

Jason Kutch (AIM)
Signal in Human Motor Unsteadiness: Detecting the Action and Activity of Muscles
(A. Bloch & A. Kuo) University of Southern California

KyungYong Lee
On Realization of Line Arrangements as Multiplier Ideals
(R. Lazarsfeld) Purdue University

John Mackay
Conformal Dimension and the Quasisymmetric Geometry of Metric Spaces
(B. Kleiner) University of Illinois at Urbana-Champaign

Jared Maruskin (AIM)
On the Dynamical Propagation of Subvolumes and on the Geometry and Variatioinal Principles of Nonholonomic Systems
(A. Bloch & D. Scheeres) San Jose State University

Yogesh More
Arc Valuations on Smooth Varieties
(K. Smith) University of Missouri

Hannah Robbins
Finiteness of Associated Primes of Local Cohomology Modules
(M. Hochster) Wake Forest University

Susan Sierra
The Geometry of Birationally Commutative Graded Domains
(J. Stafford) University of Washington

Craig Spencer
Analytic Methods for Diophantine Problems
(T. Wooley) Institute for Advanced Study

Joe Stubbs
Potent Elements and Tight Closure in Artinian Modules
(M. Hochster) University of Texas-Austin

Giancarlo Urzua
Arrangements of Curves and Algebraic Surfaces
(I. Dolgachev) University of Massachusetts at Amherst

Diane Vavrichek
Accessibility and JSJ Decompositions of Groups
(G. P. Scott) The State University of New York

Bo Yang
Application of Perturbation Methods to Pricing Credit and Equity Derivatives
(E. Bayraktar) Morgan Stanley