Algebra, Geometry and Combinatorics Day (AlGeCom) is a one day, informal meeting of mathematicians from the University of Illinois, Purdue University, IUPUI, Loyola University Chicago , DePaul University, University of Notre Dame, and nearby universities, with interests in algebra, geometry and combinatorics (widely interpreted).

Further details will be posted here as they become available. You may contact the University of Notre Dame organizer Alexander Diaz-Lopez ( Or you may contact the University of Illinois organizers Hal Schenck and Alexander Yong, or the Purdue organizers Uli Walther and Saugata Basu or IUPUI organizer Evgeny Mukhin, or the Loyola organizer Peter Tingley or the DePaul organizer Chris Drupieski.

Date:   April 30, 2016

Location: Department of Mathematics at the University of Notre Dame.

Registration is free.

To register, email the local organizer Alexander Diaz-Lopez ( by April 15.

Limited travel support is available for graduate students. To apply, email Alexander Diaz-Lopez ( by March 10 with: the name of your university, the name of your advisor, a summary of your research interests, a summary of your anticipated travel expenses, and whether you plan to participate in the poster session. Funding decisions will be made by March 15, 2016.

For a map, click

All talks will be in 127 Hayes-Healy Center.

There will be a poster session in 125 Hayes-Healy Center.


Mihai Ciucu (IU Bloomington)
Jim Haglund (UPenn)
Jenna Rajchgot (Michigan)
Dylan Rupel (Notre Dame)


Coffee and pastries          9-10am  (Math Lounge, Hurley Hall 255)


Jim Haglund 10:00-10:55am

Title: Combinatorial Problems Involving Macdonald Polynomials

Abstract: Macdonald polynomials are symmetric functions in a set of
variables X which also depend on a partition and two parameters q,t.   Long
recognized as an important object in algebraic combinatorics, they play an
increasing role in several other areas including representation theory, knot
invariants, and algebraic geometry .  In this talk we give a survey of open
combinatorial problems associated to these polynomials.

Dylan Rupel 11:30am-12:25pm

Title: Cluster Algebras and the Geometry of Quiver Grassmannians

Abstract: Cluster algebras have risen to prominence as the correct
algebraic/combinatorial language for describing recursions and
integrality/positivity phenomena appearing in many areas of mathematics.  In
this talk I will describe a connection between cluster algebras and quiver
representations where we will see that recursively computed cluster
variables are generating functions describing some geometry of quiver
Grassmannians.  From here I will describe a combinatorial construction of
these cluster variables and discuss conjectural implications of this for the
geometry of quiver Grassmannians.

Lunch       (see below for details)   12:30-2:00pm

Mihai Ciucu 2:00-2:55pm

Title: Lozenge tilings with gaps in a 90 degree wedge domain with
mixed boundary conditions

Abstract: We consider a triangular gap of side two in a 90 degree
angle on the triangular lattice with mixed boundary conditions: a
constrained, zig-zag boundary along one side, and a free lattice line
boundary along the other. We study the interaction of the gap with the
corner as the rest of the angle is completely filled with lozenges. We
show that the resulting correlation is governed by the product of the
distances between the gap and its three images in the sides of the
angle. This provides evidence for a unified way of understanding the
interaction of gaps with the boundary under mixed boundary conditions,
which we present as a conjecture. Our conjecture is phrased in terms
of the steady state heat flow problem in a uniform block of material
in which there are a finite number of heat sources and sinks. This new
physical analogy is equivalent in the bulk to the electrostatic
analogy we developed in previous work, but arises as the correct one
for the correlation with the boundary.

The starting point for our analysis is an exact formula we prove for
the number of lozenge tilings of certain trapezoidal regions with
mixed boundary conditions, which is equivalent to a new,
multi-parameter generalization of a classical plane partition
enumeration problem (that of enumerating symmetric, self-complementary
plane partitions).

Jenna Rajchgot    3:05-4:00pm

Title: Three combinatorial formulas for type A quiver polynomials and

Abstract: A quiver is a finite directed graph and a representation of a quiver is an
assignment of vector space to each vertex and linear map to each arrow. Once
the vector spaces at each vertex have been fixed, the space of
representations is an algebraic variety. This variety carries an action of a
product of general linear groups, which acts by change of basis.

I'll focus on the setting where the quiver's underlying graph is a type A
Dynkin diagram, and discuss results on the geometry and combinatorics of the
associated orbit closures (a.k.a. quiver loci). I'll show that
each quiver locus is isomorphic, up to smooth factor, to a patch of a
Schubert variety, and explain how orbit closure containment is determined by
Bruhat order on the symmetric group. I'll also describe combinatorial
formulas for multidegrees and K-polynomials. This is joint work with Ryan
Kinser and Allen Knutson.

Poster session and informal discussions:   4:00-5:00pm


Lunch: There are numerous lunch options within walking distance,
the closest being the restaurants in the LaFortune Student Center,
just steps away from Hayes-Healy. See the attached document for

Dinner: ~5:15pm We will have a subsidized banquet for registered
participants at the Oak Room, Notre Dame. We will walk over from
Hayes-Healy Center at 5:00pm, just after the poster session ends.


Local Organizers:
 Alexander Diaz-Lopez (,
 David Galvin (,
 Sam Evens (

Getting to Notre Dame:
The South Bend Airport (SBN) is 15 minutes away from Notre
Dame; you can then take a taxi from the airport to your hotel (about $20 if your hotel is
close to Notre Dame). There is a CoachUSA bus that runs from both major Chicago airports, O’hare
(ORD) and Midway (MDW), to Notre Dame for $75 roundtrip.
There is an AMTRAK in South Bend (SOB) about
15 minutes away from Notre Dame. You would then need to take a cab or Uber
 to your hotel.

The closest parking to the math buildings (Hayes-Healy and Hurley) is the C1
lot, south of the Notre Dame Stadium. The Visitor Lot South, and Bulla Lot are alternative
options. Here a local map; the conference is at Hayes-Healy Center.

The Ivy Court Inn and Suites (574-277-6500) and Suburban Extended Stay Hotel
(574-968-4737) are holding blocks of rooms for the nights of the 29th and 30th under the
name “ALGECOM” and “Notre Dame ALGECOM”, respectively. Ivy Court is within
walking distance of Notre Dame; its price is $99 plus 13% tax per night. Extended Stay (7
minutes drive to Notre Dame) price is $54 plus 13% tax. Please make your own
reservations and let us know you have done so.
Childcare:  Parents attending the conference and looking for childcare may
find a useful reference.