## MATH IU EDU VERRILL WALLPAPER

Koszul Duality for Multigraded Algebras. The congruence extension property, the ideal extension property, and ideal semigroups. Extreme elements in semigroups. Inverse semigroups on the 2-cell. Research Interests Teichmuller theory; rational billiards; and related questions involving ergodic theory, algebraic geometry, and Hilbert modular varieties.

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Absolute Z-sets and the Z-set absorption property.

## PhD Graduates

Homomorphisms of compact semigroups. Differential simplicity and complete integral closure.

On the relative K2 of non-commutative local rings. Current IU students Contact our advisor. Graphs and number theory. Some lifting problems in arithmetic equivalence. Refining the Characterization of Projective Graphs. Texas Bradley Gubser Aug. Invariants of Legendrian products.

# Department of Mathematics: Indiana University Bloomington

Banach space valued stochastic differential equations. Research Interests nonlinear partial differential equations; Navier-Stokes equations; fluid mechanics; iiu analysis; scientific computing. Book Embeddings of Graphs. Irreducible elements in compact topological lattices. A new condition for arithmetic equivalence. The congruence extension property, the ideal extension property, and ideal semigroups. Research Interests algebraic topology; geometric topology; surgery theory.

A Paley-Wiener theorem for all two and three-step Nilpotent Lie groups. Noah Snyder Associate Professor, Mathematics nsnyder1 indiana.

# PhD Graduates | LSUMath

Spaces of order arcs in hyperspaces of subcontinua. Geodetic graphs and convexity. Homogenization of Nonlinear Partial Differential Equations. Stability in Dynamical Polysystems. Unavoidable minors of graphs of large type. A necessary and sufficient condition that a set be homeomorphic to a plane region bounded by a finite number of nonintersecting circles.

Research Interests algebraic number theory; algebraic geometry; algebraic K-theory; algebraic groups; algebraic combinatorics. Shouhong Wang Professor, Mathematics showang indiana. Existence and uniqueness theorems for some white noise integral equations. Approximation numbers of bounded linear operators. Valery Lunts Professor, Mathematics vlunts edh.

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## An internationally recognized mathematics program

Modules and rings of integers in the Cayley algebra. Prof at SW Texas St.

Research Interests differential geometry; geometric aspects of mah theory and random walks. Structural results for matroids. A natural Lp-metric for spaces composed of probability measures with p-th moment. The class group in binary quadratic orders.