# Webinar

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'''Rekha R. Thomas''' (University of Washington)
'''''When Two Cameras Meet a Cubic Surface'''''
The set of images captured by an arrangement of pinhole cameras is + * Tuesday, November 10, 5pm Central European Time (UTC+1): [https://www.timeanddate.com/worldclock/converter.html?iso=20201110T160000&p1=234&p2=25&p3=270&p4=3999 Other time zones]
'''Rekha R. Thomas''' (University of Washington)
'''''When Two Cameras Meet a Cubic Surface'''''
The set of images captured by an arrangement of pinhole cameras is usually modeled by the multiview variety. The true set is in fact a semialgebraic subset of this variety, arising from the physical restriction that cameras can only image points in front of them. For a pair of cameras, the minimal problem in this semialgebraic setting is given by 5 point pairs, which even in general position, can fail to have a "chiral" reconstruction. I will describe how the combinatorics and arithmetic information of this minimal case is carried by a cubic surface with 27 real lines.
Joint work with Sameer Agarwal, Andrew Pryhuber and Rainer Sinn - usually modeled by the multiview variety. The true set is in fact a + - semialgebraic subset of this variety, arising from the physical + - restriction that cameras can only image points in front of them. For + - a pair of cameras, the minimal problem in this semialgebraic setting + - is given by 5 point pairs, which even in general position, can fail to + - have a "chiral" reconstruction. I will describe how the combinatorics + - and arithmetic information of this minimal case is carried by a cubic + - surface with 27 real lines. + -
+ - Joint work with Sameer Agarwal, Andrew Pryhuber and Rainer Sinn +

## SAGA - Seminar on Applied Geometry and Algebra

Over the last years there has been an immense growth of nonlinear models across the mathematical sciences and its applications to other disciplines. This is fueled by recent theoretical advances in understanding systems of multivariate polynomial equations and inequalities, development of efficient software solving such systems, and an increased awareness of these tools. SIAM SAGA features talks on algebraic geometry and its links to other mathematical branches -- such as combinatorics, algebraic topology, commutative algebra, convex and discrete geometry, tensors and multilinear algebra, number theory, representation theory, and symbolic and numerical computation --, focusing on a variety of applications -- including robotics, optimization, statistics, machine learning, complexity theory, cryptography, coding theory, computer vision, biology, economics, among many others.

• Finally, you will receive a confirmation email that you became a member.

Upcoming Talks All seminars take place on the 2nd Tuesday of every month at 5pm CET (UTC+1).

• Tuesday, November 10, 5pm Central European Time (UTC+1): Other time zones
Rekha R. Thomas (University of Washington)
When Two Cameras Meet a Cubic Surface
The set of images captured by an arrangement of pinhole cameras is usually modeled by the multiview variety. The true set is in fact a semialgebraic subset of this variety, arising from the physical restriction that cameras can only image points in front of them. For a pair of cameras, the minimal problem in this semialgebraic setting is given by 5 point pairs, which even in general position, can fail to have a "chiral" reconstruction. I will describe how the combinatorics and arithmetic information of this minimal case is carried by a cubic surface with 27 real lines.
Joint work with Sameer Agarwal, Andrew Pryhuber and Rainer Sinn

• Tuesday, December 8, 5pm Central European Time (UTC+1):
Camilla Hollanti (Aalto University)

• Tuesday, January 12, 5pm Central European Time (UTC+1):

• Tuesday, February 9, 5pm Central European Time (UTC+1):
Bernd Sturmfels (MPI MiS Leipzig, UC Berkeley)

Format The seminars are held on Zoom:

• 45 minutes of presentation, incl. questions
• informal discussion

Participants can ask questions in the chat or use the raise-hand tool. The chair will bring forward these questions during and after the talk, and may ask you to unmute yourself to participate in the discussion. Please note that you will be recorded if you activate your audio or video during the seminar.

Each Zoom meeting is provided by SIAM. The webinars will be recorded and posted in a SI(AG)^2 playlist on SIAM’s YouTube account.

Organizers