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Counting Surfaces: Combinatorics, Matrix Models and Algebraic Geometry

The problem of enumerating maps (a map is a set of polygonal "countries" on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, ... etc. This problem has been studied by many communities of researchers, mostly combinatorists, probabilists, and physicists. Since 1978, physicists have invented a method called "matrix models" to address that problem, and many results have been obtained.<br/>Besides, another important problem in mathematics and physics (in particular string theory), is to count Riemann surfaces. Riemann surfaces of a given topology are parametrized by a finite number of real parameters (called moduli), and the moduli space is a finite dimensional compact manifold or orbifold of complicated topology. The number of Riemann surfaces is the volume of that moduli space. More generally, an

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{Counting Surfaces: Combinatorics, Matrix Models and Algebraic Geometry

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<html>
   <head>
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      <link
         rel="stylesheet"
         href="https://unpkg.com/tachyons@4.12.0/css/tachyons.min.css"
         />
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   <body>
      <div class="flex flex-column justify-center w-100 ph3 normal lh-copy pt1">
            <div class="tc">
               <img src="https://i5.walmartimages.com/dfw/8822aef6-7abe/k2-_f4ee767f-a90a-4f70-be39-71e5d7b238a0.v1.jpg">
               <h3>4 equal payments</h3>
               <h4 class="gray">Buy what you love and split the cost. It's that easy. </h4>
            </div>
            <ul>
            <b>
               <li>Add item(s) to your cart.</li>
               <li>
                  Add items to checkout and choose 
                  <image height="14" width="auto" src="https://i5.walmartimages.com/dfw/8822aef6-7abe/k2-_f4ee767f-a90a-4f70-be39-71e5d7b238a0.v1.jpg"></image>
               </li>
               <li>Enter your debit or credit card information. </li>
               <li>Your first payment is taken when the order is processed, and the remaining 3 are automatically taken every two weeks.</li>
            </b>
            </ul>
            <p class="gray">Please note that a higher initial payment may be required for some purchases. Pay later in 4 <a href="https://cdn.klarna.com/1.0/shared/content/legal/terms/0/en_ca/paylaterin4" target="_blank">terms</a> available here. For Quebec residents, these Pay Later 4 <a href="https://cdn.klarna.com/1.0/shared/content/legal/terms/0/en_ca/paylaterin4_quebec" target="_blank">terms</a> are applicable. </p>
      </div>
   </body>
</html>

<!DOCTYPE html>
<html lang="en">
  <head>
    <meta charset="UTF-8" />
    <meta name="viewport" content="width=device-width, initial-scale=1" />
    <link
      rel="stylesheet"
      href="https://unpkg.com/tachyons@4.12.0/css/tachyons.min.css"
    />
    <style>
      body,
      html {
        font-family: 'Everyday Sans', Arial, sans-serif;
      }

      li {
        margin-bottom: 0.5rem;
      }
    </style>
    <title>Walmart Installment Plan</title>
  </head>

  <body>
    <div class="col-container w-100 normal lh-copy pt1">
      <div class="col tc">
        <img
          width="35%"
          src="https://i5.walmartimages.com/dfw/8822aef6-971e/k2-_ed78b905-6394-4f88-a805-ab299123f2cc.v1.png"
          alt="Walmart Installment Plan"
        />

        <h3>Shop today, take time to pay</h3>
        <p>
          Split your purchase into 6 equal installments*  /
          <a
            href="https://i5.walmartimages.ca/dfw/8822aef6-d3f1/k2-_417f32f7-5074-45a6-b23d-5d5b3039e5b8.v1.pdf"
            target="_blank"
            rel="noopener noreferrer"
          >
            Terms and Conditions apply
          </a>
        </p>

        <h4>Here's how it works</h4>
        <ul class="tl">
          <li>Spend $199.99 or more on walmart.ca**</li>
          <li>Select Installment Plan at checkout</li>
          <li>
            Pay with your Walmart Rewards Mastercard. If you don't have one,
            click "Apply Now".
          </li>
        </ul>

        <h4>Details</h4>
        <p>
          Your qualifying purchase will be split into 6 equal monthly
          installments charged to your Walmart Rewards Mastercard. If your items
          ship on separate dates, each shipment will be converted to a separate
          Installment Plan.
        </p>

        <h4>Don't have a Walmart Rewards Mastercard?</h4>
        <p>
          Apply now and upon approval use your new account to enjoy the
          convenience of an Installment Plan on eligible purchases*. Purchased
          items must appear on a single receipt totaling $199.99 or more (before
          taxes, discounts, Walmart Reward Dollar™ redemptions, and
          shipping/delivery fees)∆
        </p>

        <p>
          *See
          <a
            href="https://www.walmart.ca/cp/shop/installment-plan/6000204340202?icid=Glass_PIP_FinancingOptions_WRMC_LearnHow_TermsConditions2_WM"
            target="_blank"
            rel="noopener noreferrer"
          >
            Terms and Conditions
          </a>
          for full details
        </p>

        <p>
          ** Eligible Installment Plan purchases are excluded from earning
          Walmart Reward Dollars™. Walmart Gift Cards and Walmart Reward
          Dollars™ cannot currently be used on Installment Plan transactions.
         
        </p>

        <p>
          ∆ All new credit card applications are subject to approval by
          Fairstone Bank of Canada.
        </p>

        <div class="pt3">
          <a
            href="https://www.walmart.ca/en/cp/installment-plan/6000204340202?icid=Glass_PIP_FinancingOptions_WRMC_LearnHow_ApplyNow_WM"
            target="_blank"
            rel="noopener noreferrer"
          >
            <button
              class="pv2 ph3 sans-serif bg-blue white bn no-underline br-pill f6 pointer b"
              type="button"
            >
              Apply now
            </button>
          </a>
        </div>
      </div>
    </div>
  </body>
</html>

Counting Surfaces: Combinatorics, Matrix Models and Algebraic Geometry

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