Melissa Zhang





Contact Information

she/her/hers

Department of Mathematics, UC Davis
One Shields Ave.
Davis, CA 95616-8633
U.S.A.

Office: MSB 2142

@melissa-zhang.bsky.social



About me

I am an Assistant Professor of Mathematics at UC Davis.

In my research, I build and use algebraic tools to study problems and phenomena in low-dimensional topology. In particular, I am interested in the following:

Of course, I am also interested in other areas of mathematics, especially areas adjacent to my research. Outside of mathematics, I like creating music (piano, guitar, singing), arts and crafts (painting, knitting), physical activities where you just translate yourself (hiking, swimming, skating, kayaking), and baking (point at anything at a bakery and I can make a worse version). I enjoy these activities in video games as well.

[CV, updated February 2024]



Papers



Materials from Talks

Slides from some past talks

[JMM2024 Bridge Trisections with Divides]

Lecture Series on Annular Khovanov Homology

In August 2021, I gave a series of four lectures at the Perspectives on quantum link homology theories workshop organized by Lukas Lewark and Claudius Zibrowius and hosted by the University of Regensburg.

Videos of the lectures are available on their website:
[Videos]

Lecture 1: Basics of annular Khovanov homology
[slides]

Lecture 2: AKh and periodic links
[slides]

Lecture 3: sl(2) action on AKh, annular Khovanov-Lee homology
[slides]

Lecture 4: A further sampling of applications of AKh
[slides]

In Fall 2022, I organized a learning seminar at SLMath called [Homotopy Types in Low-Dimensional Topology]. Click on the link to visit the webpage containing resources for this seminar.



[Teaching]

If you are currently in one of my classes, go back to the top of the page and click on the link on the main menu bar corresponding to your course.

In my teaching, my first goal is to pique students' interest in the content, so that learning becomes a means to satisfy curiosity. In the classroom, I am currently focusing on active learning techniques, and like to give my students the time to think about questions — to ask and to answer — during our class meetings. I aim to support my students as a whole persons, as I recognize that everyone has unique struggles and needs which need to be resolved for learning to occur most efficiently.

Past courses at UC Davis:

In Fall 2024, I am currently teaching a graduate topics course in Khovanov homology and related invariants. See the [MAT280] course webpage for my continually updating lecture notes.

Winter Quarter 2024: Fall Quarter 2023: Spring Quarter 2023: Winter Quarter 2023:

Other Stuff



[Math Code]



Family

My partner Alex Wein is also a mathematician.
My sister-in-law Nicole Wein is a theoretical computer scientist.
My sister-in-law Natasha Wein is an artist. She works wonders with resin too.
My sister-in-law² Maya Hladisova is a designer.



[Round Animals]

I've been painting a lot of round animals.

[Mathematical Riddles]

I'm slowly curating my favorite mathematical riddles.

[Puzzles for K.]

These are some puzzles I worked on with an awesome middle schooler during the first year of the pandemic.

[5-minute talk timer]

[3-second talk timer demo]



[Bulk-delete Watch Later Playlist]

Sometimes I don't want to watch the dregs of my "Watch later" playlist and just want to delete them. But YouTube doesn't give you an easy way to do this. You can use AutoIt to bulk-delete unwatched videos on your YouTube "Watch later" playlist.

[Chatbot Recipes]