The 2026 Talbot Workshop will bring together senior researchers with around thirty early career mathematicians — graduate students and postdocs — for a week in an intensive and informal setting. Talbot has been a tradition for more than twenty years; each workshop since 2004 has focused on a topic that, at the time, brought participants to the forefront of topology research. The primary purpose of the workshop is research training and professional development: the goal is for junior researchers to teach each other about a contemporary research topic under the guidance of two more senior experts in the topic. Participants will give talks on a predetermined focused research area and develop a trusting and collaborative relationship with each other and the mentors. Workshop attendees will include mathematicians from a variety of institutions and backgrounds to promote the formation of new collaborative and pedagogical ties, all while exposing students and postdocs to an area of vibrant contemporary mathematics research. The focus on a single research topic, the collective nature — mentors and participants sharing meals, housing, and activities for a week — and graduate student organization make the Talbot Workshops unique among mathematics events. The workshop syllabus and notes from the talks will be posted on the workshop’s website: https://sites.google.com/view/talbotworkshop/current-talbot. This award reflects NSF's statutory mission and has been deemed worthy of sup