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| -rw-r--r-- | content/awards-grants.tex | 6 | ||||
| -rw-r--r-- | content/contact.tex | 5 | ||||
| -rw-r--r-- | content/contributed.tex | 10 | ||||
| -rw-r--r-- | content/education.tex | 19 | ||||
| -rw-r--r-- | content/invited.tex | 15 | ||||
| -rw-r--r-- | content/othertalks.tex | 14 | ||||
| -rw-r--r-- | content/positions.tex | 19 | ||||
| -rw-r--r-- | content/publications.bib | 113 | ||||
| -rw-r--r-- | content/publications.tex | 10 | ||||
| -rw-r--r-- | content/research.tex | 0 | ||||
| -rw-r--r-- | content/submitted.bib | 11 | ||||
| -rw-r--r-- | content/submitted.tex | 4 | ||||
| -rw-r--r-- | content/workshops.tex | 35 |
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diff --git a/content/awards-grants.tex b/content/awards-grants.tex new file mode 100644 index 0000000..91e640c --- /dev/null +++ b/content/awards-grants.tex @@ -0,0 +1,6 @@ +\textbf{Buncher Graduate and Faculty Fellows Research Collaboration Fund}\dotfill 2018\\ +\hphantom{@}(with Boris Bukh) +\begin{itemize} + \item Provides support for a faculty member and a graduate student to spend time in Israel at the Technion Institute with the intent of building long term research collaborations between the two universities. + The funding provides travel support for the faculty member to spend one week in Haifa and for the graduate student to stay on for 1--2 months working in the relevant Technion laboratory. +\end{itemize} diff --git a/content/contact.tex b/content/contact.tex new file mode 100644 index 0000000..bc971f5 --- /dev/null +++ b/content/contact.tex @@ -0,0 +1,5 @@ +6201 Wean Hall\\ +Carnegie Mellon University\\ +Pittsburgh, PA 15213\\ +\texttt{cocox@andrew.cmu.edu}\\ +\url{math.cmu.edu/~cocox}% diff --git a/content/contributed.tex b/content/contributed.tex new file mode 100644 index 0000000..6060590 --- /dev/null +++ b/content/contributed.tex @@ -0,0 +1,10 @@ +\begin{itemize} + \item Inverting the Tur\'an problem. \textit{ICGT}. Lyon, France, Jul.\ 2018. + \item Nearly orthogonal vectors (poster). \textit{Building Bridges II}. Budapest, Hungary, Jul.\ 2018. + \item Inverting the Tur\'an problem. \textit{MIGHTY LIX}. Morgantown, WV, Apr.\ 2018. + \item A degree sequence variant of Ramsey's theorem. \textit{Connections in Discrete Mathematics}. Vancouver, Canada, Jun.\ 2015. + \item Coupled choosability with separation. \textit{Rocky Mountain--Great Plains Graduate Research Workshop in Combinatorics}. Ames, IA, Jun.\ 2015. + \item Potential Ramsey numbers. \textit{Rocky Mountain--Great Plains Graduate Research Workshop in Combinatorics}. Denver, CO, Jul.\ 2014. + \item Normally regular digraphs resulting from Cayley graphs (poster). \textit{SACNAS National Conference}. San Antonio, TX, Oct.\ 2013. + \item Isospectral drums and cospectral graphs. \textit{MAA Mathfest}. Hartford, CT, Aug.\ 2013. +\end{itemize} diff --git a/content/education.tex b/content/education.tex new file mode 100644 index 0000000..92212a1 --- /dev/null +++ b/content/education.tex @@ -0,0 +1,19 @@ +\textbf{Doctor of Philosophy} in Algorithms, Combinatorics and Optimization\dotfill $\operatorname{\mathbb{E}}[\text{GRAD}]=2020+\varepsilon$\\ +\hphantom{@}@ Carnegie Mellon University, Pittsburgh, PA. +\begin{itemize} + \item Major professor: Boris Bukh. +\end{itemize} + +\textbf{Master of Science} in Mathematics\dotfill 2015\\ +\hphantom{@}@ Iowa State University, Ames, IA. +\begin{itemize} + \item Thesis: ``Ordered and partially-ordered variants of Ramsey's theorem.'' + \item Major professor: Derrick Stolee. +\end{itemize} + +\textbf{Bachelor of Science} in Mathematics\dotfill 2014\\ +\hphantom{@}@ Iowa State University, Ames, IA. +\begin{itemize} + \item Thesis: ``Isospectral drums and cospectral graphs.'' + \item Thesis advisor: Steve Butler. +\end{itemize} diff --git a/content/invited.tex b/content/invited.tex new file mode 100644 index 0000000..3b1aa07 --- /dev/null +++ b/content/invited.tex @@ -0,0 +1,15 @@ +\begin{itemize} + \item Algorithmic re-proofs of some Ramsey numbers. \textit{Iowa State University Discrete Mathematics Seminar}. Ames, IA, Mar.\ 2019. + \item Small antipodal spherical codes. \textit{Carnegie Mellon University CS Theory Seminar}. Pittsburgh, PA, Oct.\ 2018. + \item A fractional version of Haemers' bound. \textit{AMS Special Session on Graph Theory}. Newark, DE, Sep.\ 2018. + \item Inverting the Tur\'an problem. \textit{Iowa State University Discrete Mathematics Seminar.} Ames, IA, Jul.\ 2018. + \item Nearly orthogonal vectors. \textit{Technion Combinatorics Seminar.} Haifa, Israel, Jun.\ 2018. + \item Nearly orthogonal vectors. \textit{Hebrew University of Jerusalem Combinatorics Seminar.} Jerusalem, Israel, Jun.\ 2018. + \item A fractional version of Haemers' bound. \textit{Ben-Gurion University Combinatorics Seminar.} Be'er Sheva, Israel, Jun.\ 2018. + \item Nearly orthogonal vectors. \textit{Iowa State University Discrete Mathematics Seminar.} Ames, IA, Mar.\ 2018. + \item Ramsey numbers on the Boolean lattice. \textit{AMS Special Session on Structural and Computational Graph Theory}. Raleigh, NC, Nov.\ 2016. + \item Ramsey numbers for partially-ordered sets. \textit{Carnegie Mellon University ACO Seminar}. Pittsburgh, PA, Feb.\ 2016. + \item Ramsey numbers of ordered hypergraphs. \textit{AMS Special Session on Extremal and Stuctural Graph Theory}. Las Vegas, NV, Apr.\ 2015. + \item Ramsey numbers of ordered hypergraphs. \textit{University of Colorado Denver Discrete Mathematics Seminar}. Denver, CO, Mar.\ 2015. + \item Ordered Ramsey numbers of loose paths and $k$-uniform matchings. \textit{Iowa State University Discrete Mathematics Seminar}. Ames, IA, Oct.\ 2014. +\end{itemize} diff --git a/content/othertalks.tex b/content/othertalks.tex new file mode 100644 index 0000000..014aecd --- /dev/null +++ b/content/othertalks.tex @@ -0,0 +1,14 @@ +\begin{itemize} + \item Nearly orthogonal vectors. \textit{CMU Graduate Student Seminar}. Pittsburgh, PA, Dec.\ 2018. + \item When angles get into a car crash. \textit{CMU Graduate Student Seminar}. Pittsburgh, PA, Nov.\ 2018. + \item Poly-nom-nom-nom-ials. \textit{CMU Graduate Student Seminar}. Pittsburgh, PA, Sep.\ 2018. + \item High-dimensional hi-jinks. \textit{CMU Graduate Student Seminar}. Pittsburgh, PA, Aug.\ 2018. + \item Shannon Capacity. \textit{CMU Graduate Student Seminar}. Pittsburgh, PA, Mar.\ 2018. + \item Sperner's lemma and applications. \textit{CMU Graduate Student Seminar}. Pittsburgh, PA, Feb.\ 2018. + \item You just have to look at it from the right angle. \textit{CMU Graduate Student Seminar}. Pittsburgh, PA, Oct.\ 2017. + \item Triangles can cut cake. \textit{Western PA ARML}. Pittsburgh, PA, Mar.\ 2017. + \item 1 hat, 2 hat, red hat, blue hat. \textit{CMU Graduate Student Seminar}. Pittsburgh, PA, Feb.\ 2017. + \item The mathematics of juggling. \textit{CMU Graduate Student Seminar}. Pittsburgh, PA, Sep.\ 2016. + \item Hat guessing games and applications. \textit{Western PA ARML}. Pittsburgh, PA, Jan.\ 2016. + \item The mathematics of juggling. \textit{Western PA ARML}. Pittsburgh, PA, Sep.\ 2015. +\end{itemize} diff --git a/content/positions.tex b/content/positions.tex new file mode 100644 index 0000000..48a8538 --- /dev/null +++ b/content/positions.tex @@ -0,0 +1,19 @@ +\textbf{Teaching assistant}\dotfill 2015--Cur\\ +\hphantom{@}@ Carnegie Mellon University, Pittsburgh, PA. +\begin{itemize} + \item Instructor --- Concepts of mathematics (21-127) + \item TA --- Mathematical studies algebra I (21-237), Matrix theory (21-242), Multidimensional calculus (21-268), Calculus I (21-115), Discrete mathematics (21-228), Concepts of mathematics (21-127) +\end{itemize} + +\textbf{REU graduate research mentor}\dotfill 2015\\ +\hphantom{@}@ Iowa State University, Ames, IA. +\begin{itemize} + \item Worked with four undergraduate students on problems about mathematical juggling. + \item The papers ``A generalization of Eulerian numbers via rook placements'' and ``Counting prime juggling patterns'' are a result of this research workshop. +\end{itemize} + +\textbf{Teaching assistant}\dotfill 2014--2015\\ +\hphantom{@}@ Iowa State University, Ames, IA. +\begin{itemize} + \item TA --- Elementary differential equations (MATH 267), Calculus I (MATH 165). +\end{itemize} diff --git a/content/publications.bib b/content/publications.bib new file mode 100644 index 0000000..d6e8d63 --- /dev/null +++ b/content/publications.bib @@ -0,0 +1,113 @@ +@Article{briggscox17, + author = {Joseph Briggs and Christopher Cox}, + title = {Inverting the {T}ur{\' a}n problem}, + abstract = {Classical questions in extremal graph theory concern the asymptotics of $\operatorname{ex}(G, \mathcal{H})$ where $\mathcal{H}$ is a fixed family of graphs and $G=G_n$ is taken from a "standard" increasing sequence of host graphs $(G_1, G_2, \dots)$, most often $K_n$ or $K_{n,n}$. Inverting the question, we can instead ask how large $|E(G)|$ can be with respect to $\operatorname{ex}(G,\mathcal{H})$. We show that the standard sequences indeed maximize $|E(G)|$ for some choices of $\mathcal{H}$, but not for others. Many interesting questions and previous results arise very naturally in this context, which also, unusually, gives rise to sensible extremal questions concerning multigraphs and non-uniform hypergraphs.}, + + keywords = {pub}, + journal = {Discrete Mathematics}, + year = {2019}, + month = {Jul.}, + number = {7}, + volume = {342}, + pages = {1865-1884}, +} + +@Article{Bukh2018, + author = {Boris Bukh and Christopher Cox}, + title = {On a fractional version of {H}aemers' bound}, + abstract = {In this note, we present a fractional version of Haemers' bound on the Shannon capacity of a graph, which is originally due to Blasiak. This bound is a common strengthening of both Haemers' bound and the fractional chromatic number of a graph. We show that this fractional version outperforms any bound on the Shannon capacity that could be attained through Haemers' bound. We show also that this bound is multiplicative, unlike Haemers' bound.}, + journal = {IEEE Transactions on Information Theory}, + year = {2018}, + keywords = {pub}, +} + +@Article{Cox2018, + author = {Christopher Cox and Derrick Stolee}, + title = {Ramsey Numbers for Partially-Ordered Sets}, + journal = {Order}, + year = {2018}, + month = {Nov.}, + keywords = {pub}, + volume = {35}, + number = {3}, + pages = {557-579}, +} + +@Article{BCDHKLMMNPS15choose, + author = {Berikkyzy, Zhanar and Cox, Christopher and Dairyko, Michael and Hogenson, Kirsten and Kumbhat, Mohit and Lidick{\'y}, Bernard and Messerschmidt, Kacy and Moss, Kevin and Nowak, Kathleen and Palmowski, Kevin and Stolee, Derrick}, + title = {{$(4,2)$}-choosability of planar graphs with forbidden substructures}, + journal = {Graphs and Combinatorics}, + year = {2017}, + volume = {33}, + number = {4}, + pages = {751-787}, + month = {Jul.}, + keywords = {pub}, + owner = {Chris}, + timestamp = {2015.08.05}, + url = {http://arxiv.org/abs/1512.03787}, +} + +@Article{BBCDLP15euler, + author = {Banaian, Esther and Butler, Steve and Cox, Christopher and Davis, Jeffrey and Landgraf, Jacob and Ponce, Scarlitte}, + title = {A generalization of {E}ulerian numbers via rook placements}, + journal = {Involve}, + year = {2017}, + volume = {10}, + number = {4}, + pages = {691-705}, + month = {Mar.}, + keywords = {pub}, + owner = {Chris}, + url = {http://arxiv.org/abs/1508.03673}, +} + +@Article{BBCDLP15prime, + author = {Banaian, Esther and Butler, Steve and Cox, Christopher and Davis, Jeffrey and Landgraf, Jacob and Ponce, Scarlitte}, + title = {Counting prime juggling patterns}, + journal = {Graphs and Combinatorics}, + year = {2016}, + volume = {32}, + number = {5}, + pages = {1675-1688}, + month = {Sep.}, + keywords = {pub}, + owner = {Chris}, + url = {http://arxiv.org/abs/1508.05296} +} +@Article{CS16orram, + Title = {Ordered {R}amsey numbers of loose paths and matchings}, + Author = {Cox, Christopher and Stolee, Derrick}, + Journal = {Discrete Mathematics}, + Year = {2016}, + Month = {Feb.}, + Number = {2}, + Pages = {499-505}, + Volume = {339}, + + Abstract = {For a $k$-uniform hypergraph $G$ with vertex set $\{1,\ldots,n\}$, the ordered Ramsey number $\OR{t}{G}$ is the least integer $N$ such that every $t$-coloring of the edges of the complete $k$-uniform graph on vertex set $\{1,\ldots,N\}$ contains a monochromatic copy of $G$ whose vertices follow the prescribed order. +Due to this added order restriction, the ordered Ramsey numbers can be much larger than the usual graph Ramsey numbers. +We determine that the ordered Ramsey numbers of loose paths under a monotone order grows as a tower of height two less than the maximum degree in terms of the number of edges. +We also extend theorems of Conlon, Fox, Lee, and Sudakov [Ordered Ramsey numbers, arXiv:1410.5292] on the ordered Ramsey numbers of 2-uniform matchings to provide upper bounds on the ordered Ramsey number of $k$-uniform matchings under certain orderings.}, + Keywords = {pub}, + Owner = {Chris}, + Timestamp = {2015.05.05}, + Url = {http://www.sciencedirect.com/science/article/pii/S0012365X15003477} +} + +@Article{CDDKRT15hanabi, + author = {Cox, Christopher and De Silva, Jessica and DeOrsey, Philip and Kenter, Franklin and Retter, Troy and Tobin, R. Joshua}, + title = {How to make the perfect fireworks display: {T}wo strategies for {H}anabi}, + journal = {Mathematics Magazine}, + year = {2015}, + volume = {88}, + number = {5}, + pages = {323-336}, + month = {Dec.}, + abstract = {The game of \emph{Hanabi} is a multi-player cooperative card game which has many similarities to a mathematical `hat guessing game.' In \emph{Hanabi}, players do not know the cards in their own hand and must rely on the actions of the other players to communicate information. + +This paper presents two strategies for \emph{Hanabi}. Results from computer simulation demonstrate that both strategies perform well. In particular, one strategy achieves a perfect score of 25 points 75 percent of the time.}, + keywords = {pub}, + owner = {Chris}, + timestamp = {2015.05.05}, +} diff --git a/content/publications.tex b/content/publications.tex new file mode 100644 index 0000000..72527c1 --- /dev/null +++ b/content/publications.tex @@ -0,0 +1,10 @@ +\begin{itemize} + \item J.\ Briggs, C.\ Cox. ``Inverting the Tur\'an problem,'' \emph{Discrete Mathematics}, vol.\ 342, no.\ 7, pp.\ 1865--1884, Jul.\ 2019. + \item B.\ Bukh, C.\ Cox. ``On a fractional version of Haemers' bound,'' \emph{IEEE Transactions on Information Theory}, Dec.\ 2018 (early access). + \item C.\ Cox, D.\ Stolee. ``Ramsey numbers for partially-ordered sets,'' \emph{Order}, vol.\ 35, no.\ 3, pp.\ 557--579, Nov.\ 2018. + \item Z.\ Berikkyzy, C.\ Cox, M.\ Dairyko, K.\ Hogenson, M.\ Kumbhat, B.\ Lidick\'y, K.\ Messerschmidt, K.\ Moss, K.\ Nowak, K.\ Palmowski, D.\ Stolee. ``$(4,2)$-choosability of planar graphs with forbidden substructures,'' \emph{Graphs and Combinatorics}, vol.\ 33, no.\ 4, pp.\ 751--787, Jul.\ 2017. + \item E.\ Banaian, S.\ Butler, C.\ Cox, J.\ Davis, J.\ Landgraf, S.\ Ponce. ``A generalization of Eulderian numbers via rook placements,'' \emph{Involve}, vol.\ 10, no.\ 4, pp.\ 691--705, Mar.\ 2017. + \item E.\ Banaian, S.\ Butler, C.\ Cox, J.\ Davis, J.\ Landgraf, S.\ Ponce. ``Counting prime juggling patterns,'' \emph{Graphs and Combinatorics}, vol.\ 32, no.\ 5, pp.\ 1675--1688, Sep.\ 2016. + \item C.\ Cox, D.\ Stolee. ``Ordered Ramsey numbers of loose paths and matchings,'' \emph{Discrete Mathematics}, vol.\ 339, no.\ 2, pp.\ 499--505, Feb.\ 2016. + \item C.\ Cox, J.\ De Silva, P.\ DeOrsey, F.\ Kenter, T.\ Retter, R.J.\ Tobin. ``How to make the perfect fireworks display: Two strategies for Hanabi,'' \emph{Mathematics Magazine}, vol.\ 88, no.\ 5, Dec.\ 2015. +\end{itemize} diff --git a/content/research.tex b/content/research.tex new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/content/research.tex diff --git a/content/submitted.bib b/content/submitted.bib new file mode 100644 index 0000000..39b698d --- /dev/null +++ b/content/submitted.bib @@ -0,0 +1,11 @@ +@Article{Bukh2018a, + author = {Boris Bukh and Christopher Cox}, + title = {Nearly orthogonal vectors and small antipodal spherical codes}, + abstract = {How can $d+k$ vectors in $\mathbb{R}^d$ be arranged so that they are as close to orthogonal as possible? In particular, define $\theta(d,k):=\min_X\max_{x\neq y\in X}|\langle x,y\rangle|$ where the minimum is taken over all collections of $d+k$ unit vectors $X\subseteq\mathbb{R}^d$. In this paper, we focus on the case where $k$ is fixed and $d\to\infty$. In establishing bounds on $\theta(d,k)$, we find an intimate connection to the existence of systems of ${k+1\choose 2}$ equiangular lines in $\mathbb{R}^k$. Using this connection, we are able to pin down $\theta(d,k)$ whenever $k\in\{1,2,3,7,23\}$ and establish asymptotics for general $k$. The main tool is an upper bound on $\mathbb{E}_{x,y\sim\mu}|\langle x,y\rangle|$ whenever $\mu$ is an isotropic probability mass on $\mathbb{R}^k$, which may be of independent interest. Our results translate naturally to the analogous question in $\mathbb{C}^d$. In this case, the question relates to the existence of systems of $k^2$ equiangular lines in $\mathbb{C}^k$, also known as SIC-POVM in physics literature.}, + date = {2018-03-08}, + eprint = {1803.02949v1}, + eprintclass = {math.CO}, + eprinttype = {arXiv}, + file = {online:http\://arxiv.org/pdf/1803.02949v1:PDF}, + keywords = {sub}, +} diff --git a/content/submitted.tex b/content/submitted.tex new file mode 100644 index 0000000..7b13ae3 --- /dev/null +++ b/content/submitted.tex @@ -0,0 +1,4 @@ +\begin{itemize} + \item J.\ Briggs, C.\ Cox. ``The query complexity of locating monochromatic matchings and trees,'' arXiv:1904.00246. + \item B.\ Bukh, C.\ Cox. ``Nearly orthogonal vectors and small antipodal spherical codes,'' arXiv:1803.02949. +\end{itemize} diff --git a/content/workshops.tex b/content/workshops.tex new file mode 100644 index 0000000..bce433b --- /dev/null +++ b/content/workshops.tex @@ -0,0 +1,35 @@ +\textbf{Informal analysis seminar}\dotfill Feb.\ 2018\\ +\hphantom{@}@ Kent State University, Kent, OH. +\begin{itemize} + \item Attended the lecture series: ``Packing a torus with circles'', ``Tensegrities: why things don't fall down'' and ``A degenerate isoperimetric problem in the plane with applications to a bi-stable Hamiltonian system''. +\end{itemize} + +\textbf{Summer school on random graphs and probabilistic methods}\dotfill Jun.\ 2017\\ +\hphantom{@}@ The Fields Institute, Toronto, CA. +\begin{itemize} + \item Attended a two week summer school comprised of four lecture series: ``Ten lectures on random graphs'', ``Ten lectures on random graph processes'', ``Random spanning trees and forests'' and ``Randomness for and against computation''. +\end{itemize} + +\textbf{Graduate Research Workshop in Combinatorics (GRWC)}\dotfill Jun.\ 2015\\ +\hphantom{@}@ Iowa State University, Ames, IA. +\begin{itemize} + \item Participated in an experimental research program for graduate students in discrete mathematics (see \url{https://sites.google.com/site/rmgpgrwc/}). The program consisted of about 35 graduate students in addition to faculty and postdocs working on problems presented by the students. Many collaborations have continued to be productive outside the workshop. +\end{itemize} + +\textbf{Discrete Mathematics Working Seminar}\dotfill 2014--2015\\ +\hphantom{@}@ Iowa State University, Ames, IA. +\begin{itemize} + \item Worked with a group of graduate students, postdocs and professors on research problems in discrete mathematics. This collaboration has resulted in the paper ``$(4,2)$-choosability of planar graphs with forbidden structures.'' +\end{itemize} + +\textbf{Graduate Research Workshop in Combinatorics (GRWC)}\dotfill Jul.--Aug.\ 2014\\ +\hphantom{@}@ University of Denver and University of Colorado Denver, Denver, CO. +\begin{itemize} + \item Participated in an experimental research program for graduate students in discrete mathematics (see \url{https://sites.google.com/site/rmgpgrwc/}). The program consisted of about 30 graduate students in addition to faculty and postdocs working on problems presented by the students. Many collaborations have continued to be productive outside the workshop. +\end{itemize} + +\textbf{NSF REU}\dotfill Jun.--Aug.\ 2013\\ +\hphantom{@}@ Iowa State University, Ames, IA. +\begin{itemize} + \item Worked under the direction of Sung-Yell Song on projects in algebraic graph theory, focusing on the classification of Cayley graphs and the construction of normally regular digraphs. +\end{itemize} |