January 29, 2026 (Thursday), 4:10-5:15 PM<\/p>\n
Dr. Christine Berkesch, University of Minnesota<\/p>\n
Geometry and Multigraded Polynomials<\/span><\/span><\/strong><\/p>\n In a graded polynomial, all terms have the same degree. For instance, $x^3+x^2y+z^3$ is graded of degree 3. There is a long and rich history tying the geometry of projective varieties and the algebra of graded polynomials and modules. Multigraded polynomials have even more structure. For instance, $x_0^2y_0^3 \u00a0+ x_1^2y_1^3$ is bigraded of degree (2,3): it is graded of degree 2 with respect to the x-variables and degree 3 with respect to the y-variables. Recent work has led to new frameworks for leveraging geometry (including toric geometry and symplectic geometry) to understand multigraded algebra. I will give a survey of the history and recent progress.\u00a0<\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":" January 29, 2026 (Thursday), 4:10-5:15 PM Dr. Christine Berkesch, University of Minnesota Geometry and Multigraded Polynomials In a graded polynomial, all terms have the same degree. For instance, $x^3+x^2y+z^3$ is graded of degree 3. There is a long and rich history tying the geometry of projective varieties and the algebra of graded polynomials and modules….<\/p>\n","protected":false},"author":208,"featured_media":1675,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[7,4],"tags":[],"acf":[],"jetpack_featured_media_url":"https:\/\/as.vanderbilt.edu\/math\/wp-content\/uploads\/sites\/69\/2026\/02\/Untitled-300-x-300-px.jpg","_links":{"self":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/1677"}],"collection":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/users\/208"}],"replies":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/comments?post=1677"}],"version-history":[{"count":1,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/1677\/revisions"}],"predecessor-version":[{"id":1678,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/1677\/revisions\/1678"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media\/1675"}],"wp:attachment":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media?parent=1677"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/categories?post=1677"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/tags?post=1677"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}