{"id":48875,"date":"2024-08-20T16:06:08","date_gmt":"2024-08-20T20:06:08","guid":{"rendered":"https:\/\/engineering.jhu.edu\/ams\/?post_type=news&p=48875"},"modified":"2025-09-17T13:42:18","modified_gmt":"2025-09-17T17:42:18","slug":"new-senior-lecturer-explores-algebraic-combinatorics","status":"publish","type":"news","link":"https:\/\/engineering.jhu.edu\/ams\/news\/new-senior-lecturer-explores-algebraic-combinatorics\/","title":{"rendered":"New senior lecturer explores algebraic combinatorics\u00a0\u00a0"},"content":{"rendered":"

Su Ji Hong<\/a> joined the Department of Applied Mathematics and Statistics on July 1 <\/span>from Yale University where she was also a senior lecturer<\/span>.<\/span> Her research <\/span>focuses on algebraic combinatorics, lattice polytopes, cluster algebras, and triangulations.\u00a0<\/span>In this Q&A, she discusses the complexities and real-world implications of mathematical structures, as well as her excitement to become part of the Hopkins Engineering team.\u00a0\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

Tell us a little about yourself.\u202f\u00a0\u00a0<\/strong><\/p>\n

I am originally from Jeju, South Korea. Jeju is the biggest island in Korea, and it\u2019s a beautiful vacation spot. I moved to California when I was in middle school and stayed there until I graduated from California Lutheran University with bachelor\u2019s degrees in mathematics and physics. I then moved to Lincoln, Nebraska, for a Ph<\/span>.<\/span>D<\/span>.<\/span> program in Mathematics. After graduating, I spent three years at Yale University as a lecturer.<\/span>\u00a0<\/span><\/p>\n

 <\/p>\n

Describe your research.\u202f\u00a0\u00a0<\/strong><\/p>\n

My research lies under the umbrella of algebraic combinatorics. Combinatorics is a study of counting and arranging and the objects that I study usually come from algebraic structures. I have worked with real Schur roots, the integer decomposition properties of certain types of polytopes, box-ball systems, etc. Some of these objects can be very difficult to define. My goal has been to describe them in a simpler way so that I can better understand them and hopefully use alternative representations to prove certain properties. For example, instead of using the representation theory definition of real Schur roots, we can use non-self-intersecting curves.<\/span>\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

What are some of the real-world applications of your research?\u00a0\u00a0<\/strong><\/p>\n

I study discrete and\/or algebraic structures that do not appear in the real world. But the core approach I take, using multiple representation to better understand the object, is applicable to real-world problems. For example, we can convert the problem of assigning medical residents to the hospitals into a graph matching problem. Additionally, my research falls under the umbrella of discrete mathematics, the study of discrete structures. Discrete mathematics encompasses many fields of mathematics, including combinatorics, graph theory, and cryptography, widely utilized in computer science, credit card security, algorithms, and other domains.<\/span>\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

What drew you to this field and focus area?\u202f\u00a0\u00a0<\/strong><\/p>\n

I have always enjoyed puzzle solving, and mathematics is a subject that allows me to solve many puzzles. In graduate school, I took a discrete mathematics course and enjoyed doing every homework problem. Of those problems, the ones that excited me the most were those stemming from algebra. I found algebraic combinatorics to be the type of puzzle that I enjoy solving. Algebraic combinatorics studies algebraic structures (or discrete structures) with combinatorial tools (or tools from algebra). Combinatorial proofs can be simple and mind-blowing.<\/span>\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

What excites you about bringing this work to Johns Hopkins?\u202f\u00a0\u00a0<\/strong><\/p>\n

One aspect of discrete mathematics I love the most is its approachability. Undergraduate students can understand and work on discrete mathematics research problems due to their simplicity. I mentored an undergraduate research project on the box-ball system at Yale University, and students began working on the problem soon into the summer program. I would like to get to know the brilliant students at JHU and I am excited to work with them!<\/span>\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

What are some of your goals for this first year at JHU?\u202f\u00a0\u00a0<\/strong><\/p>\n

I think discrete mathematics is so fun and beautiful. I want to share my excitement with students, and hopefully they will come to appreciate the subject as much as I do!<\/span>\u00a0<\/span><\/p>\n

As a senior lecturer, one of my responsibilities is to assist postdocs with their instruction. I have completed several teaching-related programs, such as Project NExT and the Faculty Teaching Academy at Yale University. I enjoy discussing different teaching approaches and strategies. My goal is to be someone they can turn to with any teaching difficulties. While I may not have all the solutions, I am committed to brainstorming with them to find solutions!<\/span>\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

Anything else we should know? Any fun facts?\u202f\u00a0\u00a0\u00a0<\/strong><\/p>\n

I like embroidery and crochet. If there are any craft clubs, let me know! A fun fact about me is that before moving to Baltimore, I always moved east. From South Korea to California (we flew over the Pacific Ocean) to Nebraska to Connecticut. This is my first time moving \u201cwest,\u201d and I\u2019m very excited!<\/span>\u00a0<\/span><\/p>\n

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