# overview
My research focuses on noncommutative geometry, K-theory of operator algebras, index theory, topology and analysis of manifolds, and geometric group theory.

# keywords[]
4903 Numerical And Computational Mathematics

# educationAndTraining[].organization.label
Stony Brook University - (Stony Brook, New York, United States)

# educationAndTraining[].organization.label
Mathematical Sciences Research Institute - (Berkeley, California, United States)

# publications[].label
Hyperbolic groups admit proper affine isometric actions on lp-spaces

# publications[].label
K-theory for the maximal Roe algebra of certain expanders

# publications[].label
Uniform embeddability and exactness of free products

# publications[].label
Contractible manifolds with exotic positive                    scalar curvature behavior

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

# publications[].label
The Novikov conjecture for algebraic K-theory of the group algebra over the ring of Schatten class operators

# publications[].label
Higher rho invariants and the moduli space of positive scalar curvature metrics

# publications[].label
Localization algebras and the coarse Baum--Connes conjecture

# publications[].label
The Novikov conjecture, the group of volume preserving diffeomorphisms and Hilbert-Hadamard spaces

# publications[].label
Baum-Connes conjecture and coarse geometry

# publications[].label
Delocalized Eta Invariants, Algebraicity, and K-Theory of Group C*-Algebras

# publications[].label
K-thorie quantitative pour les algbres doprateurs

# publications[].label
The coarse BaumConnes conjecture and groupoids

# publications[].label
Quantitative K-theory and the Knneth formula for operator algebras

# publications[].label
Volume growth and positive scalar curvature

# publications[].label
Higher invariants in noncommutative geometry

# publications[].label
The Equivariant Coarse Novikov Conjecture and Coarse Embedding

# publications[].label
Geometrization of the Strong Novikov Conjecture for residually finite groups

# publications[].label
The coarse geometric Novikov conjecture and uniform convexity

# publications[].label
The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space

# publications[].label
The Novikov Conjecture for Groups with Finite Asymptotic Dimension

# publications[].label
Dynamic asymptotic dimension: relation to dynamics, topology, coarse geometry, and C-algebras

# publications[].label
Asymptotic Fredholm Modules, Vector Bundles with Small Variation and a Nonvanishing Theorem for K-Theoretic Indices

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

# publications[].label
Cyclic Cohomology and Higher Indexes for Noncompact Complete Manifolds

# publications[].label
A finite-dimensional approach to the strong Novikov conjecture

# publications[].label
Positive scalar curvature, higher rho invariants and localization algebras

# publications[].label
Index formulas for geometric Dirac operators in Riemannian foliations

# publications[].label
Higher index theory for certain expanders and Gromov monster groups, I

# publications[].label
Non-commutative Geometry, Index Theory and Mathematical Physics

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

# publications[].label
Higher index theory of elliptic operators and geometry of groups

# publications[].label
Additivity of Higher Rho Invariants and Nonrigidity of Topological Manifolds

# publications[].label
The Novikov conjecture and geometry of Banach spaces

# publications[].label
Uniform Embeddings into Hilbert Space and a Question of Gromov

# publications[].label
Finite part of operator                    K                    theory for groups finitely embeddable into Hilbert space and the degree of nonrigidity of manifolds

# publications[].label
Noncommutative Geometry of Discrete Groups

# publications[].label
Metric sparsification and operator norm localization

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

# publications[].label
Boundary Amenability of Groups and Positive Scalar Curvature

# publications[].label
Addendum to Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory (J. reine angew. Math. 694 (2014), 129178)

# publications[].label
K-Theoretic Indices of Dirac Type Operators on Complete Manifolds and the Roe Algebra

# publications[].label
A new index theorem for monomial ideals by resolutions

# publications[].label
A notion of geometric complexity and its application to topological rigidity

# publications[].label
Positive scalar curvature and a new index theory for noncompact manifolds

# publications[].label
Discrete groups with finite decomposition complexity

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

# publications[].label
Taming 3-manifolds using scalar curvature

# publications[].label
Higher index theory for certain expanders and Gromov monster groups, II

# publications[].label
An analytic Grothendieck Riemann Roch theorem

# publications[].label
Operator norm localization for linear groups and its application to K-theory

# publications[].label
Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory

# publications[].label
Bounded rigidity of manifolds and asymptotic dimension growth

# publications[].label
The coarse BaumConnes conjecture for spaces which admit a uniform embedding into Hilbert space

# publications[].label
Zero-in-the-spectrum conjecture, positive scalar curvature and asymptotic dimension

# publications[].label
A relative higher index theorem, diffeomorphisms and positive scalar curvature

# publications[].label
The coarse Novikov conjecture and Banach spaces with Property (H)

# publications[].label
The Baum-Connes conjecture for hyperbolic groups

# publications[].label
Higher  invariant is an obstruction to the inverse being local

# researcherOn[].label
Great Plains Operator Theory Symposium 2019-

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
K-theory of Operator Algebras and Its Applications to Geometry and Topology

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
Higher Invariants of Elliptic Operators and Applications

# researcherOn[].awardedBy.label
Directorate for Mathematical & Physical Sciences - (Arlington, Virginia, United States)

# researcherOn[].label
Conference: International Workshop on Operator Theory and its Applications 2018

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
K-Theory of Operator Algebras and Its Applications

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
Operator K-Theory and its Applications to Geometry and Topology

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# streetAddress
Texas A&M University; Mathematics; 3368 TAMU