
Dustin Clausen Permanent professor
Mathematician with interests in algebraic K-theory, number theory, analytic geometry, functional analysis, and homotopy theory. PhD from MIT in 2013 under the supervision of Jacob Lurie.
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Duality and linearization for p-adic lie groups
( PDF )
2025-06-22, -
The reductive Borel-Serre compactification as a model for unstable
algebraic K-theory
( PDF )
2023-11-21, -
Descent and vanishing in chromatic algebraic $K$-theory via group
actions
( PDF )
2022-11-08, -
Hyperdescent and étale K-theory
( PDF )
2021-03-18, -
K-theory and topological cyclic homology of henselian pairs
( PDF )
2020-07-20, -
Remarks on $K(1)$-local $K$-theory
( PDF )
2020-05-12, -
Descent in algebraic $K$-theory and a conjecture of Ausoni-Rognes
( PDF )
2017-11-22, -
A K-theoretic approach to Artin maps
( PDF )
2017-04-03, -
A short proof of telescopic Tate vanishing
( PDF )
2017-01-04, -
p-adic J-homomorphisms and a product formula
( PDF )
2012-01-28,
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Scheme Theory
Avec Lars Hesselholt
https://web.math.ku.dk/~larsh/teaching/S2022_A/schemes.pdf -
Condensed Mathematics and Complex Geometry
Avec Peter Scholze
https://people.mpim-bonn.mpg.de/scholze/Complex.pdf -
Riemann Surfaces
Lecture 1: Review of holomorphic functions
Lecture 2: Algebraic functions and analytic continuation
Lecture 3: Structured surfaces
Lecture 4: More examples of Riemann surfaces
Lecture 5: Statement of the main theorems
Lecture 6: Local structure of holomorphic maps
Lecture 7: The Riemann sphere, take one: algebra
Lecture 8: The Riemann sphere, take two: geometry
Lecture 9: The Riemann sphere, take three: geometry continued
Lecture 10: The hyperbolic plane
Lecture 11: Riemann surfaces uniformized by the Riemann sphere and the complex plane
Lecture 12: Elliptic curves from lattices
Lecture 13: Fundamental groups and universal covers
Lecture 14: Holomorphic one-forms and vector fields
Lecture 15: Uniformizations of elliptic curves, and moduli
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Cyclotomic Fields
Lecture 1: Basic definitions, and the irreducibility of cyclotomic polynomials
Lecture 2: Second proof of the irreducibility of cyclotomic polynomials
Lecture 3: Introduction to rings of integers
Lecture 4: Geometry of numbers
Lecture 5: The volume of a number field
Lecture 6: The ring of integers of cyclotomic fields, and ideal theory
Lecture 7: A pre-analysis discussion of zeta functions
Lecture 8: Dirichlet L-series at s=1
Lecture 9: Dirichlet's theorem on primes in arithmetic progressions
Lecture 10: The analytic class number formula
Lecture 11: The minus part of the class group
Lecture 12: Gauss periods
Lecture 13: Quadratic reciprocity and the sign of the Gauss sum
Lecture 14: General Gauss sums
Lecture 15: The maximal ideal factorization of Gauss sums
Lecture 16: Stickelberger's theorem and Herbrand's theorem
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Algebraic de Rham Cohomology
Lecture 1: de Rham cohomology of real manifolds
Lecture 2: Interlude on D(R)
Lecture 3: Interlude on sheaves with values in D(Z)
Lecture 4: de Rham cohomology of complex manifolds
Lecture 5: Grothendieck's theorem, part 1
Lecture 6: Grothendieck's theorem, part 2
Lecture 7: Kahler differentials, smooth maps, and the de Rham complex
Lecture 8: Derived quasi-coherent sheaves
Lecture 9: Globalization and Deligne's theorem on degeneration
Lecture 10: Deligne's theorem, part 2
Lecture 11: de Rham cohomology in characteristic p: pathological?
Lecture 12: Equivariant de Rham cohomology: set-up and definition
Lecture 13: Totaro's theorem on Hodge cohomology of classifying stacks
Lecture 14: Chern classes and Thom classes
Lecture 15: Cycle classes and deformation to the normal bundle
Lecture 16: Poincaré duality