Julianne Vega

jve229's picture
  • Graduate Student
  • Primary Instructor
722 Patterson Office Tower
Research Interests:

In 2017, I completed my Masters with Bert Guillou on Quillen's fiber lemma for posets. I am currently working towards my Doctorate in Topological Combinatorics with my advisor, Benjamin Braun. My research interests lie in simplicial complexes, graphs, posets, and equivariance.  

In my current projects, my overall interests involve learning about properties of graphs. To do so, I create spaces, i.e. simplicial complexes, that encapsulate the properties that I am interested in, and analyze the characteristics of the space. 



  • Haj\'os-type constructions and neighborhood complexes, joint with Benjamin Braun      Submitted, arXiv:1812.07991
  • Matching complexes of trees and applications of the matching tree algorithm, joint with Marija Jelic, Helen Jenne, and Alex Mcdonough     Submitted, arXiv:1905.10560
  • A combinatorial positivity phenomenon in Elser's Gaussian-cluster percolation model, joint with Galen Dorpalen-Barry, Cyrus Hettle, David Livingston, Jeremy Martin, George Nasr, and Hays Whitlatch     Submitted, arXiv:1905.11330
  • Two-matching complexes Submitted, arXiv:1909.10406
  • Homotopy type of k-matching complexes, independent/ dissertation work
  • Whitney duals of graded posets, GRWC collaboration joint with Margaret Bayer, Bennet Goeckner, Josh Carlson, Joshua Miller, Kyle Murphy, Casey Pickney, and Sung-Yell Song
  • Newton polytopes arising from Schur polynomials and Symmetric Grothendeick polynomials, GRWC collaboration joint with Maragret Bayer, Bennet Goeckner, Su Ji Hong, Tyrrell McAllister, McCabe Olsen, Casey Pickney, Martha Yip, Semin Yoo
  • Conceptual learning and sense of belonging, joint with Pooja Gupta Sidney, Benjamin Braun, and Gabrielle Eismann
  • Math Lab Co-director- Undergraduate Research Project: Matching Tree Morse Spectra for Graphs, joint with Benjamin Braun


I am fortunate to have had by first teaching experience at Burgundy Farm Country Day School a progressive, independent school in Alexandria, VA. It was there that I developed as a teacher leader and learned the importance of working with colleagues to build the best possible learning community. I took on many leadership positions, both formal and informal, that placed me at the heart of what makes Burgundy beautiful. My classroom encouraged curiosity and invited students to actively participate in their learning.  
Moving into my current position as recitation leader and primary instructor has led me to reflect and adapt my teaching to elicit the same curiosity and engagement in college students. In Fall 2018, I taught a medium-sized lecture of College Algebra (75 students). Through this experience I learned how my teaching practices can be further adapted to reach larger classes. In the past, I could have full class discussions on new topics, bringing discovery to the class as a whole, but in a larger lecture this is impractical. To emulate these constructive discussions, I provided time for individual discovery at which time I walk around and work with small groups of students. My undergraduate assistant and I work as a seamless team, answering questions that arise during work sessions. 
As an educator, I would describe myself as a constructivist and progressive teacher. I believe in supporting the growth of the whole student. At the undergraduate level this means helping them assimulate to the new demands of college life, living away from family, and growing into an independent learner. In addition, I structure my classroom to help students discover mathematics and develop a conceptual understanding of the material.  
I strive to be a community leader. As such I believe in the importance of service. I am involved in many leadership positions, both formal and informal in the department. During the 2018-2019 school year, I participated in the Inclusive Pedagogies Graduate Learning Community. I also led two efforts within our department, the Appalachian Initiative for Mathematics (AIM) and Inclusive Community Lunches, which continue to grow. 
Outside of my concerted efforts on diversity, I was the AWM vice president of our current student chapter. Along with my AWM officers, we have developed committees to incorporate the input of our members into our event planning. A consequence of that is the formation of several committees and collaborations with other student organizations in STEM fields. In August 2019, we have received the AWM student chapter award for Community Outreach. 
I am also involved in outreach programs such as Nerd Squad and Math Circle, two programs that reach out to elementary-high school students in the area to introduce them to math concepts. All of my service to the community evidences my desire to build a rich learning environment that encourages curiosity, passion, and life-long learning. 
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