I am a graduate student at Stanford University. My main interest is algebraic topology and my advisor is Soren Galatius. Before this I studied theoretical physics and mathematics at Utrecht University. My bachelor thesis was supervised by Andre Henriques and my master thesis by Ieke Moerdijk.
In 2013-2014 I am teaching Math 51 in Winter quarter. In 2012-2013 I did not teach. In 2011-2013, in spring I was a CA for Math 171, in winter I did not teach and in fall 2011 I was a CA for Math 19.
- In preparation: Homological stability for complements of closures, joint with Jeremy Miller.
- In preparation: Comparing combinatorial models for moduli space and their compactifications, joint with Daniela Egas.
- Homological stability for topological chiral homology for completions (arXiv), joint with Jeremy Miller.
- Some stable homology computations and Occam's razor for Hodge structures (arXiv, to appear in JPAA), joint with Jeremy Miller.
- Homological stability for unlinked Euclidean circles in R3 (arXiv).
- Constructing higher string operations for manifolds using radial slit configurations, June 2013 draft version.
- An elementary proof of the string topology structure of compact oriented surfaces (arXiv).
- The string topology structure of the Lie groups SU(n), U(n), Sp(n), G2 and F4, an old note doing computations in string topology.
- AJBSSTS Notes, June 20th version of the notes.
- AJOSSCS Notes, November 11th version of the notes. Also see Kyler Siegel's notes at his website.
- Higher string operations, my MSc thesis about constructing higher string operations (warning: approximately 3.5mb).
Currently, Kate Poirier from UC Berkeley and I are running the Awesome Joint Berkeley-Stanford String Topology Seminar AJBSSTS. The seminar will consist of two talks every two weeks, alternating between Stanford and Berkeley. We are finished for the academic 2011-2012 and will continue next fall. The notes appear above.
Together with Arnav Tripathy I am organizing the Thursday seminar. We are currently discussing one topic: cool stuff.
Together with Otis Chodosh I am organizing a seminar on positive scalar curvature, the Awesome Joint Otis-Sander Scalar Curvature Seminar AJOSSCS. The notes appear above.
Talks and notes
This is a list of talks that I gave at some point. Many of them have notes posted. I often start writing notes, but not always finish them, so if you want half-finished notes from one of the other talks, feel free to email me.
- December 6th, 2013, Student Topology Seminar: Mahowald's construction of HF2 as a Thom spectrum, a talk one of the most surprising theorems in topology.
- October 23rd, 2013, CUNY Topology Seminar: Topological chiral homology and homological stability for completions of En-algebras, a talk about recent joint work with Jeremy Miller and its historical background.
- June 6th, 2013, Math395: Swan's non-principal ideal, a very terse sketch of Swan's solution to questions of Steenrod about finite Moore spaces with group actions and Noether about invariant rational functions, using algebraic K-theory of group rings and a particular non-principal ideal.
- May 30th, 2013, Math395: The algebraic K-theory of algebraically closed fields, a very terse sketch of Suslin's theorem that an inclusion of algebraically closed fields induces an isomorphism on K-theory with finite coefficients.
- May 6th, 2013, Kiddie Seminar: Why my parents' home is not underwater, a talk about mathematical history, discussing Simon Stevin's work. Talk slides available on request (they're very big). There are scans of the original prints available on Google Books, e.g. De Beghinselen des Waterwichts.
- May 2nd, 2013, XKCD Seminar: Topological chiral homology and homological stability, a talk which gives an introduction to topological and chiral homology and discusses recent joint work with Jeremy Miller.
- April 23rd, 2013, Talbot workshop: Talbot talk on Morava E-theory and change-of-rings theorems, in which we define Morava E-theory and sketch the proof of the Miller-Ravenel and Morava change-of-rings theorems..
- April 8th, 2013, Copenhagen: One approach to the first two hours of string topology, in which we introduce string topology and discuss a large variety of examples. Also relevant are A plan for lectures on higher string operations and The string operation associated to a single generic radial slit configuration..
- February 27th, 2013, Topology Progress Seminar: An overview of the parametrized stable H-cobordism theorem, about the proof of PL version due to Waldhausen-Jahren-Rognes and the reduction of the smooth case to the PL case.
- February 14th and 21st, 2013, Student Topology Seminar: An introduction to BP-theory, in which we discuss the Hopf algebroid coming from MU, the construction of BP, Landweber's classification of invariant prime ideals in BP, Landweber exactness and the chromatic spectral sequence.
- December 17th, 2012, Munster Topology Seminar: The stable homology of the moduli space of highly-connected higher-dimensional complexes, in which we report on work in progress on the homology of the moduli space d-dimensional (d-1)-connected finite complexes. We compute the group completion of the homology with respect to wedge sum and discuss the possibility of homological stability for these spaces. Warning: This sketch has a number of errors and I have since changed the definitions.
- December 11th, 2012, Bonn Topology Seminar: Higher string operations and radial slit configurations, in which explain we a construction of higher string operations using radial slit configurations, preceded by a general introduction to string operations and followed by remarks about compactified string operations.
- November 28th, 2012, Student Algebraic Geometry Seminar: Milnor K-theory and geometry, a gentle introduction to Milnor K-theory through its history and examples, followed by a sketch of Totaro's identification of Milnor K-theory with a certain higher Chow group and Suslin's identification of it with the cokernel of a certain homological stabilization map.
- October 24th, 2012, Student Topology Seminar: An introduction to the Adams spectral sequence, in which we construct the Adams spectral sequence and use it to compute some stable homotopy groups of spheres at the prime 2. This is the expanded version, covering both talks.
- October 15th, 2012, Kiddie Seminar: Oriented bordism: calculation and application, an introduction to oriented bordism. It starts elementary, with the definition and calculations up to and including dimension 4. After that we change gear and calculate the full oriented bordism ring rationally and prove the Hirzebruch signature theorem.
- September 7th, 2012, Student Topology Seminar: The rank theorem in algebraic K-theory, which uses the rank filtration on the algebraic K-theory spectrum due to Rognes to compute the K-theory of finite sets.
- August 31st, 2012, Student Topology Seminar: Baas-Sullivan bordism theories, or how to construct homology from bordism.
- July 2nd, 2012, Young Topologists Meeting 2012 (Copenhagen): Radial slit configurations and string topology, a gentle introduction to Bodigheimer's radial slit configuration model of the moduli space of Riemann surface with boundary and its applications to string topology.
- June 8th, 2012, Student Topology Seminar: Exotic 7-spheres, which discusses Milnor's classical 1956 article.
- May 17th, 2012, Talbot workshop: Talbot talk on embedding calculus, the little disks operad and rational homology of embedding spaces, which explains the general relationship between context-free functors in embedding calculus and modules over the little disks operads, and apply this to prove that the rational homology of the space of reduced embeddings of a manifold into a Euclidean space depends only on the rational homology of the manifold if the Euclidean space is of sufficiently high dimension.
- April 27th, 2012, Student Topology Seminar: Talbot pretalk on Kontsevich formality of the little N-disks operad, in which I explain the proof of the Kontsevich formality theorem using Arnold's formality of configuration spaces of points in the complex plane as a guiding example. The Kontsevich formality theorem is a key ingredient in the theorems I discuss in my Talbot talk about the rational homology of embedding spaces.
- April 11th, 2012, SUMO (Stanford Undergraduate Mathematics Organisation) Seminar: Space-filling curves and the Hahn-Mazurkiewicz theorem, in which I give two examples of constructions of space-filling curves and then prove the Hahn-Mazurkiewicz theorem, which gives necessary and sufficient conditions for a subset of Euclidean space to be the image of the unit interval under a continuous map.
- March 16th, 2012, Student Topology Seminar: The space of framed functions (part 2: applications to higher Reidemeister torsion), in which discuss Igusa's definition of higher Reidemeister torsion and do some computations.
- March 9th, 2012, Student Topology Seminar: The space of framed functions (part 1: definitions and contractibility), in which I define the spaces of generalized Morse functions and framed functions and sketch Galatius' proof that the space of framed functions on any manifold in contractible.
- March 1st, 2012, Thursday seminar: Sullivan's approach to rational homotopy theory, an introduction to commutative DGA's as a model for rational homotopy types, following Bousfield and Gugenheim.
- January 9th, 2012, Lille Topology seminar: String operations for manifolds using radial slit configurations, an introduction to higher string operations and their construction using radial slit configurations.
- December 1st, 2011, Kiddie seminar: No strings attached (improved kitten-containing version), an introduction to string topology through the Goldman Bracket and the Chas-Sullivan construction.