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"A rock pile ceases to be a rock pile the moment a single man contemplates it, bearing within him the image of a cathedral."—Antoine de Saint-Exupery, The Little Prince

Shamuel (Sam) Auyeung

(This webpage will move soon). I am a 6th-year graduate student at Stony Brook University (graduating soon and off to Trinity College for a visiting position). Here is my CV. My research interests lie mainly in symplectic geometry and more specifically, I think about various Floer homology theories applied to problems concerning the interplay of algebraic and symplectic geometry. I also have interest in gauge theories, low-dimensional topology, and mathematical physics but currently, more as a "hobbyist." My advisor is Mark McLean.
I am originally from Colorado (where the above photo was taken) and before arriving at SBU, I studied math, philosophy, and ancient Greek at Calvin College.

Email: shamuel271828[dot]auyeung196883[at]math[dot]stonybrook[dot]edu (remove all the numbers)

Office: 3-104, Math Department, Stony Brook University

Research Papers

With Jin-Cheng Guu and Jiahao Hu, "On the algebra generated by \bar{\mu},\bar{\partial},\partial,\mu," Complex Manifolds; available here. Early in the process, we consulted Macaulay2; code is here.
"Local Lagrangian Floer Homology of Quasi-Minimally Degenerate Intersections," to appear in Journal of Topology and Analysis, preprint available here and a talk on the paper here.

With Eric Yu: The Krein Matrix and an Interlacing Theorem
With Joshua Ruiter and Daiwei Zhang: An Algebraic Characterization of Highly Connected 2n-Manifolds

Seminars I Co-Organize(d)

Symplectic Geometry, Gauge Theory, and Low-Dimensional Topology Seminar (Spring 2023)
Student Symplectic Seminar (Fall 2022): Weinstein domains and their symplectic invariants
RTG Student Seminar (Fall 2019): Homological Mirror Symmetry (and Spring 2020: Modular Forms but that was disrupted halfway)

Invited Talks

University of Iowa Geometry and Topology Seminar: "Adjacent Singularities, Multiplicity, and Fixed-Point Floer Cohomology"
Rutgers University, Woodward’s Research Group: "Adjacent Singularities, Multiplicity, and Fixed-Point Floer Cohomology"
Western Hemisphere Virtual Symplectic Seminar: "Local Lagrangian Floer Homology of Quasi-Minimally Degenerate Intersections"

Other (Expository) Talks I've Given

Symmetric Products and Eilenberg-MacLane Spaces
Survey of Sheaf Theoretic Approaches to Symplectic/Contact Geometry
Oriented Cobordism, Genera, and the Hirzebruch Signature Theorem (notes)
Symplectic Cohomology I: Reeb Dynamics and Viterbo Functoriality
Symplectic Cohomology II: Product Structures, Loop Spaces, and Hochschild Homology
Monodromy Zeta Functions and Adjacent Singularities
<k>-Manifolds and Framed Cobordism of Manifolds with Corners (based on Cohen-Jones-Segal)
Some Incarnations of McKay Correspondences (following McKay, Du Val)
Twisted Complexes and Split Generation (following Auroux)
Morse Theory and Hamiltonian Floer Homology (following Audin-Damian)
The de Rham Groupoid (following Goldman-Xia)

Teaching

This semester I am a TA for MAT 132.

Prior Teaching and Math/Teaching Philosophy

Notes

Condensed review for SBU's comprehensive exam; the exam fluctuates year by year. This review sheet does not cover, for example, representations.
Qualifying Exam
Introductory note from a Fall 2019 seminar on G_2 manifolds
Examples/Expository Notes

Other Interesting Resources (not written by me)

Here is a nice, short article by Henry Cohn on why symplectic geometry naturally arose from classical mechanics.
Here is a blog by Chris Wendl on symplectic and contact geometry.
Here is a mathematical interpretation of the Aharonov-Bohm effect from physics. In particular, I find it validating towards math.
Here is a brief introduction to mirror symmetry from the perspective of physicist Robbert Dijkgraaf.

Silliness

I'm not sure what to mind concerning copyright issues. But ultimately, shouldn't credit be given to Bill Watterson?